Publications in Which CSDP Has Been Used

CSDP has been used by a number of researchers to solve SDP problems arising in their research projects. The following list of references includes only published papers in which CSDP has been used to solve SDP problems as opposed to papers that simply cite CSDP as an example of a software package for solving SDP's. I've linked to the published version of the paper using the Digital Object Identifier (DOI). A subscription may be required to access the actual paper. Where possible I've also included links to freely available preprints of the papers. Please [mailto:[email protected] email] any additions or corrections.

• P. Adasme and A. Lisser A Computational Study for Bilevel Quadratic Programs using Semidefinite Relaxations European Journal of Operational Research 254(1):9-18, 2016.

• P. Adasme and A. Lisser Stochastic and semidefinite optimization for scheduling in orthogonal frequency division multiple access networks. Journal of Scheduling, 17: 445-469, 2014.

• P. Adasme, A. Lisser, and I. Soto. Robust Semidefinite Relaxations for a Quadratic OFDMA Resource Allocation Scheme. Computers & Operations Research 38:1377-1399, 2011.

• P. Adasme, A. Lisser, and I. Soto. A quadratic semidefinite relaxation approach for resource allocation in orthogonal frequency division multiple access. Networks, 59(1):3-12, 2012.

• G. Agarwal and D. Kempe. Modularity-maximizing graph communities via mathematical programming. The European Physical Journal B - Condensed Matter and Complex Systems 66(3):409-418, 2008. Preprint.

• M. Agrawal and L. S. Davis. Camera Calibration Using Spheres: a Semi-Definite Programming Approach. In Computer Vision, 2003. Proceedings. Ninth IEEE International Conference on Computer Vision. pages 782- 789, 2003. Preprint.

• N. E. Aguilera and P. Morin. Approximating Optimization Problems Over Convex Functions. Numerische Mathematik 111:1-34, 2008. Preprint.

• N. E. Aguilera and P. Morin. On Convex Functions and the Finite Element Method. SIAM Journal on Numerical Analysis 47(4):3139-3157, 2009. Preprint.

• K. Ampountolas, N. Zheng, and N. Geroliminis. Perimeter flow control of bi-modal urban road networks: A robust feedback control approach. In 2014 European Control Conference (ECC), pages 2569-2574, 2014.

• K. Ampountolas and N. Zheng. Robust control of bi-modal multi-region urban networks: An LMI optimisation approach. In 17th IEEE Conference on Inteligent Transportation Systems, pages 489-494, 2014.

• K. Ampoutolas, N. Zheng, and N. Geroliminis. Macroscopic modelling and robust control of bi-modal multi-region urban road networks.Transportation Research Part B: Methodological, 104:616-637, 2017.

• C. K. Anand, A. D. Bain, and A. Sharma. Optimized Sampling Patterns for Multidimensional T2 Experiments. Journal of Magnetic Resonance 197:63-70, 2009.

• M. F. Anjos, B. Ghaddar, L. Hupp, F. Liers, and A. Wiegele. Solving k-way graph partitioning problems to optimality: The impact of semidefinite relaxations and the bundle method. In Facets of combinatorial optimization, pages 355-386. Springer Verlag. Berlin 2013.

• M. F. Anjos and J. Neto. Spectral Bounds for Graph Partitioning with Prescribed Partition Sizes. Discrete Applied Mathematics 269:200-210, 2019.

• M. F. Anjos and J. Neto. A Class of Spectral Bounds for Max k-Cut Discrete Applied Mathematics 279:12-24, 2020.

• M. F. Anjos and A. Vannelli. On the Computational Performance of a Semidefinite Programming Approach to Single Row Layout Problems. In Operations Research Proceedings 2005, pages 277-282. Springer Verlag. Berlin, 2005.

• M. F. Anjos and A. Vannelli. Computing Globally Optimal Solutions for Single-Row Layout Problems Using Semidefinite Programming and Cutting Planes. INFORMS Journal on Computing 20(4):611-617, 2008. Preprint.

• M. F. Anjos and H. Wolkowicz. Strengthened Semidefinite Relaxations via a Second Lifting for the Max-Cut Problem. Discrete Applied Mathematics 119(1-2):79-106, 2002.

• M. F. Anjos and G. Yen. Provably Near-Optimal Solutions For Very Large Single-Row Facility Layout Problems. Optimization Methods & Software 24:805-817, 2009. Preprint.

• M. Ansariola. Computational Approaches for Understanding Combinatorial Gene Regulation. PhD Thesis, Oregon State University, 2018.

• M. Ansariola, M. Megraw, and D. Koslicki. IndeCut evaluates performance of network motif discovery algorithms. Bioinformatics 34(9):1514-1521, 2017.

• P. R. Arantes-Gilz, M. Joldes, C. Louembet, and F. Camps. Stable Model Predictive Strategy for Rendezvous Hovering Phases Allowing for Control Saturation To appear in Journal of Guidance, Control, and Dynamics, 2019.

• S. Ba, B.C. Chatterjee, and E. Oki. Performance of route partitioning scheme for hitless defragmentation in elastic optical networks. In 2017 International Conference on Computing, Networking and Communications (ICNC), 2017.

• R. Baber and J. Talbot. New Turan Densities For 3-Graphs. Electronic Journal of Combinatorics 19(2), #P22, 2012.

• R. Baber and J. Talbot. Hypergraphs Do Jump. Combinatorics, Probability and Computing 20:161-171, 2011.

• R. Baber and J. Talbot. A Solution to the 2/3 Conjecture. SIAM Journal on Discrete Mathematics, 28(2):756-768, 2014.

• C. Bachoc and F. Vallentin. Optimality and Uniqueness of the (4, 10, 1/6) Spherical Code. Journal of Combinatorial Theory, Series A 116:195-204, 2009. Preprint.

• C. Bachoc and F. Vallentin. Semidefinite Programming, Multivariate Orthogonal Polynomials, and Codes in Spherical Caps. European Journal of Combinatorics 30:625-637, 2009.

• J. Balogh, P. Hu, B. Lidicky, and H. Liu. Upper bounds on the size of 4- and 6-cycle-free subgraphs of the hypercube. European Journal of Combinatorics 35:75-85, 2014.

• J. Balogh, P. Hu, B. LIDICKÝ, O. PIKHURKO, B. UDVARI, and J. VOLEC. Minimum Number of Monotone Subsequences of Length 4 in Permutations. Combinatorics, Probability and Computing, 24:658-679, 2015.

• J. Balogh, F. C. Clemen, and B. Lidicky. Maximum Number of Almost Similar Triangles in the Plane Computational Geometry 105:101880, 2022.

• J. Balogh, F. C. Clemen, and B. Lidicky. Solving Turán's tetrahedron problem for the ℓ 2 ℓ_2‐norm To Appear in Journal of the London Mathematical Society, 2022.

• X. Bao, N. V. Shainidis, and M. Tawarmalani. Semidefinite relaxations for quadratically constrained quadratic programming: A review and comparisons. Mathematical Programming 129(1):129-157, 2011.

• S. Behrends, R. Hübner, A.Schöbel.Norm bounds and underestimators for unconstrained polynomial integer minimization. Mathematical Methods of Operations Research, 87 (1):73-107, 2018.

• P. Bennet, A. Dudek, B. Lidicky, and O. Pikhurko. Minimizing the number of 5-cycles in graphs with given edge-density To Appear in Combinatorics, Probability and Computing, 2020.

• A. Billionnet, S. Elloumi, and A. Lambert. Using a Conic Bundle Method to Accelerate Both Phases of a Quadratic Convex Reformulation. INFORMS Journal on Computing 29(2):318-331, 2017.

• A. Billionnet, S. Elloumi, and A. Lambert. An Efficient Compact Quadratic Convex Reformulation for General Integer Quadratic Programs Computational Optimization and Applications 54:141-162, 2013.

• A. Billionnet, Sourour Elloumi, and Amélie Lambert. Extending the QCR method to general mixed-integer programs. Mathematical Programming 131:381-401, 2012.

• A. Billionnet, S. Elloumi, and A. Lambert. A Branch and Bound Algorithm for General Mixed-Integer Quadratic Programs Based on Quadratic Convex Relaxation. Journal of Combinatorial Optimization 28(2):376-399, 2014.

• A. Billionnet, S. Elloumi, and A. Lambert. Exact quadratic convex reformulations of mixed-integer quadratically constrained problems. Mathematical Programming, 158 (1-2):235-266, 2016.

• Jacek Blaszczyk, Ewa Niewiadomska-Szynkiewicz, and Michael Marks. Application of Rectangular Full Packed and Blocked Hybrid Matrix Formats in Semidefinite Programming for Sensor Network Localization. In Parallel Processing and Applied Mathematics, Proceedings of the 7th International Conferece. Lecture Notes in Computer Science 4967:649-658, 2008.

• M. Bowling, A. Ghodsi, and D. Wilkinson. Action Respecting Embedding. Proceedings of the 22nd international conference on Machine learning, pages 65-72, 2005. Preprint.

• H. C. Bravo, K. E. Lee, B. B. K. Klein, R. Klein, S. K. Iyengar, and G. Wabha. Examining the Relative Influence of Familial, Genetic, and Enviornmental Covariate Information in Flexible Risk Models. Proceedings of the National Academy of Sciences 106:8128-8133, 2009.

• M. Bruglieri, F. Maffioli, and M. Ehrgott. Cardinality Constrained Minimum Cut Problems: Complexity and Algorithms. Discrete Applied Mathematics 137(3):311-341, 2004.

• C. Buchheim, M. Montenegro, and A. Wiegele. SDP-based branch-and-bound for non-convex quadratic integer optimization. Journal of Global Optimization 73(3):485-514, 2019.

• C. Buchheim, M. De Santis, L. Palagi, and M. Piacentini. An Exact Algorithm for Nonconvex Quadratic Integer Minimization Using Ellipsoidal Relaxations. SIAM Journal on Optimization 23:1867-1889, 2013.

• C. Buchheim and A. Wiegele. Semidefinite relaxations for non-convex quadratic mixed-integer programming. Mathematical Programming 141:435-452, 2013.

• S. Burer and H. Dong. Separation and relaxation for cones of quadratic forms. Mathematical Programming 137:343-370, 2013.

• F. Camps, P. R. A> Gilz, M. Joldes, and C. Louembet. Embedding a SDP-Based Control Algorithm for the Orbital Rendezvous Hovering Phases. Presented at the 25th Saint Petersburg International Conference on Integrated Navigation Systems (ICINS), 2018.

• J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing. Universal Linear Optics. Science, 349(6249):711-716, 2015.

• A. Cerveira, A. Agra, F. Bastos, and J. Gromicho. A New Branch and Bound Method for a Discrete Truss Topology Design Problem. Computational Optimization and Applications 54:163-187, 2013.

• W. Chen, Y. Chen, K. Q. Weinberger, Q. Lu, X. Chen. Goal-Oriented Euclidean Heuristics with Manifold Learning. Proceedings of the Twenty-Seventh AAAI Conference on Artificial Intelligence, pages 173-179, 2013.

• K. K. H. Cheung. Computation of the Lasserre Ranks of Some Polytopes. Mathematics of Operations Research 32(1):88-94, 2007.

• H. Cohn and J. Woo. Three-point bounds for energy minimization. Journal of the American Mathematical Society 25:929-958, 2012.

• J. Cong and B. Liu. A metric for layout-friendly microarchitecture optimization in high-level synthesis. In DAC '12 Proceedings of the 49th Annual Design Automation Conference. Pages 1239-1244, 2012.

• L. N. Coregliano, R. F. Parente, and C. M. Sato. On the Maximum Density of Fixed Strongly Connected Subtournaments, Electronic Journal of Combinatorics, 26(1):44, 2019.

• J. Cummings, D. Dral, F. Pfender, K. Sperfeld, A. Treglown, and M. Young. Monochromatic Triangles in Three-Coloured Graphs. Journal of Combinatorial Thoery Series B 103(4):489-503, 2013.

• L. Dai and B. Xia. Smaller SDP for SOS Decomposition. Journal of Global Optimization 63:343-361, 2015.

• W. Damm, A. Mikschl, J. Oehlerking, E-R Oldergo, J. Pang, A. Platzer,M. Segelken, and B Wirtz. Automating Verification of Cooperation, Control, and Design in Traffic Applications In: Formal Methods and Hybrid Real-Time Systems, p 115-169, 2007.

• T. A. Davis, Y. C. Shin, and B. Yao. Observer-Based Adaptive Robust Control of Friction Stir Welding Axial Force. In Proceedings of the 2010 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, pages 1162-1167, 2010. Reprint.

• E. De Klerk, D. V. Pasechnik, and A. Schrijver. Reduction of Symmetric Semidefinite Programs Using the Regular *-Representation. Mathematical Programming 109(2-3):613-624, 2007. Preprint.

• E. De Klerk, D. V. Pasechnik, and R. Sotirov. On Semidefinite Programming Relaxations Of The Traveling Salesman Problem. SIAM Journal on Optimization 19(4):1559-1573, 2008.

• H. Dong. Symmetric Tensor Approximation Hierarchies for the Completely Positive Cone. SIAM Journal on Optimization, 23:1850-1866, 2013.

• H. Dong and J. Linderoth. On valid inequalities for quadratic programming with continuous variables and binary indicators. International Conference on Integer Programming and Combinatorial Optimization. Springer, 2013.

• E. Martin-Dorel and P. Roux. A reflexive tactic for polynomial positivity using numerical solvers and floating-point computations CPP 2017: Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and ProofsJanuary 2017 Pages 90-99, 2017.

• S. Drury. The Triangle Graph T6 Is Not SPN Electronic Journal of Linear Algebra, 36:90=93, 2020.

• S. Elloumi and A. Lambert. Global solution of non-convex quadratically constrained quadratic programs. Optimization Methods & Software 34(1):98-114, 2019.

• S. Elloumi, A. Lambert, and A. Lazare. Semidefinite Programming Relaxtions Through Quadratic Reformulation for Box-Constrained Polynomial Optimization Problems In 6th International Conference on Control, Decision and Information Technologies, 2019.

• S. Elloumi, A. Lambert, and A. Lazare. Solving Unconstrained 0-1 Polynomial Programs Through Quadratic Convex Reformulation Journal of Global Optimization 80.2:231.248, 2021.

• V. Falgas-Ravry and E. R. Vaughan. Applications of the Semi-Definite Method to the Turan Density Problem for 3-Graphs. Combinatorics Probability & Computing 22(1):21-54, 2013.

• M. H. C. Fampa, W. A. X. Melo, and N. Maculan. Semidefinite Relaxation for Linear Programs With Equilibrium Constraints. International Transactions in Operational Research, 20:201-212, 2012.

• D. Feng, C. Germain-Renaud, and T. Glatard Distributed Monitoring with Collaborative Prediction. 12th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing (CCGrid), 376:383, 2012.

• D. Feng, C. Germain, and T. Glatard Efficient Distributed Mnitoring with Active Collaborative Prediction. Future Generation Computing Systems 29:2272-2283, 2013.

• D. Feng and C. Germain. Fault Monitoring with Sequential Matrix Factorization. ACM Transactions on Autonomous and Adaptive Systems, 10(3):376-383, 2015.

• F. M. de Oliveira Filho and F. Vallentin. Computing Upper Bounds for the Packing Density of Congruent Copies of a Convex Body In New Trends in Intuitive Geometry, edited by Gergely Ambrus, Imre Bárány, Károly J. Böröczky, Gábor Fejes Tóth, and János Pach, 155–88. Bolyai Society Mathematical Studies. Berlin, Heidelberg: Springer Berlin Heidelberg, 2018.

• F. Flehmig and W. Marquardt. Inference of Multi-Variable Trends in Unmeasured Process Quantities. Journal of Process Control 18:491-503, 2008.

• J. M. Fry and M. Farhood. A Comprehensive Analytical Tool for Control Validation of Fixed-Wing Unmanned Aircraft. IEEE Transactions on Control Systems Technology 28(5):1785-1801, 2020.

• R. Fuentes-Loyola and V. H. Quintanna. Medium Term Hydrothermal Coordination by Semidefinite Programming. IEEE Transactions on Power Systems 18(4):1515-1522, 2003.

• F. Furini and E. Traversi. Hybrid SDP Bounding Procedure. In Proceedings of the 12th International Symposium on Experimental Algorithms, SEA 2013, Lecture Notes in Computer Science, 7933:248-259, 2013.

• L. Galli, K. Kaparis, and A. N. Letchford. Gap Inequalities for the Max-Cut Problem: A Cutting-Plane Algorithm. Lecture Notes in Computer Science 7422:178-188, 2012.

• L. Galli and A. N. Letchford A compact variant of the QCR method for quadratically constrained quadratic 0–1 programs. Optimization Letters 8:1213-1224, 2014.

• L. Galli and A. N. Letchford On the Lovász theta function and some variants. Discrete Optimization 25:159-174, 2017.

• M. Garraffa, F. Della Croce, and F. Salassa. An exact semidefinite programming approach for the max-mean dispersion problem. Journal of Combinatorial Optimization 34(1):71-93, 2017.

• A. Garulli, A. Masi, S. Paoletti, and E. Türkoglu. Clearance of flight control laws via parameter-dependent Lyapunov functions. IFAC Proceedings Volumes, 6th IFAC Symposium on Robust Control Design 42, 337–342, 2009.

• T. M. Gawlitza and H. Seidl. Computing Relaxed Abstract Semantics w.r.t. Quadratic Zones Precisely. In Proceedings of the 17th International Symposium on Static Analysis, SAS 2010, Perpignan, France. Lecture Notes in Computer Science 6337:271-286, 2011.

• T. M. Gawlitza, H. Seidl, A. Adje, S. Gaubert, and E. Goubalt. Abstract Interpretation Meets Convex Optimization. Journal of Symbolic Computation 47:1416-1446, 2012.

• E. Gethner, L. Hogben, B. Lidický, F. Pfender, A. Ruiz, and M. Young. On Crossing Numbers of Complete Tripartite and Balanced Complete Multipartite Graphs. Journal of Graph Theory 84 (4):552-565, 2017.

• B. Ghaddar, M. Anjos, and F. Liers. A Branch-and-Cut Algorithm Based On Semidefinite Programming for the Minimum k-Partition Problem. Annals of Operations Research 188:155-174, 2011. Preprint.

• K. Ghorbal, E. Goubault, and S. Putot. The Zonotope Abstract Domain Taylor1+. International Conference on Computer Aided Verification, page 627-633. Springer, 2009.

• P. R. A. Gilz, M. Joldes, C. Louembet, and F. Camps. Model Predictive Control for Rendezvous Hovering Phases Based on a Novel Description of Constrained Trajectories. IFAC-PapersOnline 50:7229–7234, 2017.

• R. Glebov, D. Kral, and J. Volec. A Problem of Erdos and Sos on 3-Graphs. The Seventh European Conference on Combinatorics, Graph Theory and Applications. CRM Series Volume 16, pages 3-8, 2013.

• R. Glebov, D. Kral, and J. Volec. A problem of Erdos and Sos on 3-Graphs. Israel Journal of Mathematics, 211(1):349-366, 2016.

• X. Goaoc, A. Hubard, R. de Joannis de Verclos, J-S Sereni, and J. Volec. Limits of Order Types. In Proceedings of the 31st International Symposium on Computational Geometry, p 300--314, 2015.

• J. Goldberger and A. Leshem. MIMO Detection for High-Order QAM Based on a Gaussian Tree Approximation. IEEE Transactions on Information Theory 57(8):4973-4982, 2011.

• C. P. Gomes, W. J. van Hoeve, and L. Leahu. The Power of Semidefinite Programming Relaxations for MAX-SAT. Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, Lecture Notes in Computer Science 3990:104-118, 2006. Preprint.

• A. Gorge, A. Lisser and R. Zorgati. Stochastic Nuclear Outages Semidefinite Relaxations. Computational Management Science 9:363-379, 2012.

• V. Golyanik and D. Stricker. Dense Batch Non-Rigid Structure form Motion in a Second. In 2017 IEEE International Conference on Applications of Computer Visions, p 254-263, 2017.

• G. Gruber and F. Rendl. Computational Experience with Stable Set Relaxations. SIAM Journal on Optimization 13:1014-1028, 2003.

• A. Grzesik, P. Hu, and J. Volec. Minimum Number of Edges That Occur in Odd Cycles. Journal of Combinatorial Theory, Series B, December 14, 2018. https://doi.org/10.1016/j.jctb.2018.12.003.

• A. Grzesik, J. Lee, B. Lidicky, and J. Volec. On Tripartite Common Graphs. Combinatorics, Probability and Computing, 1-17, 2020.

• N. Gvozdenovic, M. Laurent, and F. Vallentin. Block-diagonal Semidefinite Programming Hierarchies for 0/1 Programming. Operations Research Letters 37:27-31, 2009. Preprint.

• W. W. Hager, D. T. Phan, and H. Zhang. An exact algorithm for graph partitioning. Mathematical Programming 137:531-556, 2013.

• V. Hähnke, M. Rupp, M. Krier, F. Rippmann, and G. Schneider. Pharmacophore alignment search tool: Influence of canonical atom labeling on similarity searching. Journal of Computational Chemistry 31(15):2810-2826, 2010.

• V. Hähnke, M. Rupp, A. Hartmann, and G. Schneider. Pharmacophore Alignment Search Tool (PhAST): Significance Assessment of Chemical Similarity. Molecular Informatics, 32:625-646, 2013.

• J. Harrison. Verifying Nonlinear Real Formulas Via Sums of Squares In In: Schneider K., Brandt J. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2007. Lecture Notes in Computer Science, vol 4732. Springer, 2007.

• J. Heller and T. Pajdlaa. GpoSolver: a Matlab/C++ toolbox for global polynomial optimization. Optimization Methods and Software 31(2):405-434, 2016.

• Y. Hirai and K. Yamamoto. Balancing Weight-Balanced Trees. Journal of Functional Programming 21(3):287-307, 2011.

• W. J. van Hoeve. A Hybrid Constraint Programming and Semidefinite Programming Approach for the Stable Set Problem. Principles and Practice of Constraint Programming 2003, Lecture Notes in Computer Science, 2833:407-421, 2003. Preprint.

• W. J. van Hoeve. Exploiting Semidefinite Relaxations in Constraint Programming. Computers and Operations Research 33(10):2787-2804, 2006. Preprint.

• C. Hou, Y. Jiao, Y. Wu, and D. Yi. Relaxed Maximum-Variance Unfolding. Optical Engineering 47(7):077202-1-077202-12, 2008.

• C. Hou, Y. Wu, D. Yi, and Y. Jiao. Novel Semisupervised High-Dimensional Correspondences Learning Method. Optical Engineering 47(4):1-10, 2008.

• C. Hou, C. Zhang, Y. Wu, and Y. Jiao. Stable Local Dimensionality Reduction Approaches. Pattern Recognition 42:2054-2066, 2009.

• E. Hu, S. Chen, D. Zhang, and X. Yin. Semisupervised Kernel Matrix Learning by Kernel Propagation. IEEE Transactions on Neural Networks 21(11):1831-1841, 2010.

• E. Hu, S. Chen, J. Yu, and L. Qiao. Two-stage Nonparameteric Kernel Learning: From Label Propagation to Kernel Propagation Neurocomputing 74:2725-2733, 2011.

• D. Huang, Z. Yi, and X. Pu. Manifold-Based Learning and Synthesis. IEEE Transactions on Systems, Man, and Cybernetics-- Part B: Cybernetics 39:592-606, 2009.

• D. Huang, Z. Yi, and X. Pu. A Kernel View of Manifold Analysis for Face Images. In Proceedings of the 2008 3rd International Conference on Inteligent System and Knowledge Engineering, p 650-654, 2008.

• R. Iraji and H. Chitsaz. NUROA: A Numerical Roadmap Algorithm. 53rd Annual Conference on Decision and Control, 5359 - 5366, 2014.

• I. D. Ivanov and E. de Klerk. Parallel implementation of a semidefinite programming solver based on CSDP on a distributed memory cluster. Optimization Methods and Software Volume 25(3):405-420, 2010.

• D. Justice and A. Hero. Estimation of Message Source and Destination from Link Intercepts. IEEE Transactions on Information Forensics and Security 1(3):374-385, 2006. Preprint.

• R. Kamyar, M. M. Peet, and Y. Peet. Solving Large-Scale Robust Stability Problems by Exploiting the Parallel Structure of Polya's Theorem. IEEE Transactions on Automatic Control, 58:1931-1947, 2013.

• R. Kamyar and M. M. Peet. Decentralized computation for robust stability analysis of large state-space systems using Polya's theorem. In Proceedings of the American Control Conference, 5948-5954, 2012.

• H. Kjellberg and E. G. Lightsey. Discretized Constrained Attitude Pathfinding and Control for Satellites. Journal of Guidance, Control, and Dynamics, 36(5):1301-1309, 2013.

• H. Kjellberg and E. G. Lightsey. A Constrained Attitude Control Module for Small Satellites. In Proceedings of the 26th Annual AIAA/USU Conference on Small Satellites, 2012.

• P. M. Kleniati, P. Parpas, and B. Rustem. Decomposition-based Method for Sparse Semidefinite Relaxations of Polynomial Optimization Problems. Journal of Optimization Theory and Applications 145:289-310, 2010.

• F. W. Kong and B. Rustem. Welfare Maximizing Correlated Equilibria Using Kantorovich Polynomials With Sparsity. Journal of Global Optimization 57:251-277, 2013.

• N. Krislock, J. Malickc, and F. Roupind. Computational results of a semidefinite branch-and-bound algorithm for k-cluster. Computers & Operations Research 66:153-159, 2016.

• A. Kumagai. Extension of classical MDS to treat dissimilarities not satisfying axioms of distance. Japan Journal of Industrial and Applied Mathematics, 31:111-124, 2014.

• A. Kumagai. Spectral Dimensionality Reduction for Bregman Information. Information Geometry 2:273–282, 2019.

• L. Létocart, M-C Plateau, and G. Plateau. An efficient hybrid heuristic method for the 0-1 exact k-item quadratic knapsack problem. Pesquisa Operacional 34(1):49-72, 2014.

• L. Létocart and A. Wiegele Exact Solution Methods for the k-Item Quadratic Knapsack Problem. International Symposium on Combinatorial Optimization, 2016.

• H. Li, M.C. Robini, F. Yang, I. Magnin, and Y. Zhu. Cardiac Fiber Unfolding by Semidefinite Programming. IEEE Transactions on Biomedical Engineering, 62:582-592, 2014.

• H. Li, M. Robini, Z. Zhou, W. Tang, and Y. Zhu. Nasal Mesh Unfolding – An Approach to Obtaining 2-D Skin Templates from 3-D Nose Models. In Medical Image Computing and Computer Assisted Intervention – MICCAI 2018, edited by Alejandro F. Frangi, Julia A. Schnabel, Christos Davatzikos, Carlos Alberola-López, and Gabor Fichtinger, 163–70. Lecture Notes in Computer Science. Springer International Publishing, 2018.

• M. Li, H. Xi, and Y. Sun. Feature Extraction and Visualization of MI-EEG with L-MVU Algorithm. In World Congress on Medical Physics and Biomedical Engineering 2018, edited by Lenka Lhotska, Lucie Sukupova, Igor Lacković, and Geoffrey S. Ibbott, 68/3:835–39. Singapore: Springer Singapore, 2019.

• W. Li, Y. Ma, Q. Sun, Y. Lin, I. Jiang, B. Yu, and D. Z. Pan. OpenMPL: An Open Source Layout Decomposer IEEE 13th International Conference on ASIC, page 1-4, 2019.

• Z. Li, J. Liu, and X. Tang. Pairwise Constraint Propagation by Semidefinite Programming for Semi-Supervised Classification. In Proceedings of the 25th International Conference on Machine Learning 576-583, 2008.

• Z. Li, J. Liu, and X. Tang. Constrained Clustering via Spectral Regularization. IEEE Conference on Computer Visition and Pattern Recognition, 421-428, 2009.

• B. Lidicky and F. Pfender. Semidefinite Programming and Ramsey Numbers SIAM Journal on Discrete Mathematics 35(4):2328-2344, 2021.

• C. H. R. Lima, U. Lall, T. Jabara, and A. G. Barnston. Statistical Prediction of ENSO from Subsurface Sea Temperature Using a Nonlinear Dimensionality Reduction. Journal of Climate 22:4501-4519, 2009.

• H. Lin, S. Song, and J. Yang. 2018. Ship Classification Based on MSHOG Feature and Task-Driven Dictionary Learning with Structured Incoherent Constraints in SAR Images. Remote Sensing 10(2):190, 2018.

• B. Liu and S. X. D. Tan. Minimum Decoupling Capacitor Insertion in VLSI Power/Ground Supply Networks by Semidefinite and Linear Programs. IEEE Transactions on Very Large Scale Integration (VLSI) Systems 15(11):1284-1287, 2007.

• D. Liu, B. Yu, S. Chowdhury, and D. Z. Pan. Incremental Layer Assignment for Critical Path Timing. In DAC '16 Proceedings of the 53rd Annual Design Automation Conference, p 85, 2016.

• D. Liu, B. Yu, S. Chowdhury, and D. Z. Pan. Incremental Layer Assignment for Timing Optimization. ACM Transactions on Design Automation of Electronic Systems 22(4):1-25, 2017.

• N. Liu, F. Bai, J. Yan, B. Zhang, Z. Chen, and W. Y. Ma. Supervised Semi-definite Embedding for Email Data Cleaning and Visualization. In Web Technologies Research and Development - AP Web 20, Lecture Notes in Computer Science 3399:972-982, 2005.

• Y. J. Liu, T. Chen, Y. Yao. Nonlinear process monitoring and fault isolation using extended maximum variance unfolding. Journal of Process Control, 24(6):880-891, 2014.

• G. Liuzzi, M. Locatelli, and V. Piccialli. A new branch-and-bound algorithm for standard quadratic programming problems. Optimization Methods & Software 34(1):79-97, 2019.

• M. Locatelli. Improving upper bounds for the clique number by non-valid inequalities Mathematical Programming 150(2):511-525, 2015.

• Y. Ma, W. Zhong, S. Hu, J-R Gao, J. Kuang, J. Miao, and B. Yu. A Unified Framework for Simultaneous Layout Decomposition and Mask Optimization IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems. 39(12):5069-5082, 2020.

• H. van Maaren and L. van Norden. Sums of Squares, Satisfiability and Maximum Satisfiability. In Theory and Applications of Satisfiability Testing, Lecture Notes in Computer Science 3569:294-308, 2005. Preprint.

• H. van Maaren, L. van Norden, and M. H. H. Heule. Sums of Squares Based Approximation Algorithms for MAX-SAT. Discrete Applied Mathematics 156:1754-1779, 2008. Preprint.

• M. Madrigal and A. D. Quintana. Semidefinite Programming Relaxations for {0,1}-Power Dispatch Problems. In Power Engineering Society Summer Meeting, pages 697-702, IEEE, 1999. Preprint.

• T. Magesacher. Optimal Intra-Symbol Transmit Windowing for Multicarrier Modulation. In Proceedings of the International Symposium on Communications, Control and Signal Processing ISCCSP 2006, Marrakech, Morocco, March 2006.

• T. Magseacher. Spectral Compensation for Multicarrier Communication. IEEE Transactions on Signal Processing 55(7):3366-3379, 2007.

• T. Magesacher, P. Odling, and P. O. Borjesson. Optimal Intersymbol Transmit Windowing for Multicarrier Modulation. Proceedings of the Seventh Nordic Signal Processing Symposium, 70-73, 2006.

• J. Malick and F. Roupin. Solving k -cluster problems to optimality with semidefinite programming. Mathematical Programming 136:279-300, 2012.

• J. Malick and F. Roupin. Numerical Study of Semidefinite Bounds for the k-cluster Problem. Electronic Notes in Discrete Mathematics 36(1):399-406, 2010.

• E. Martin-Dorel and P. Roux A reflexive tactic for polynomial positivity using numerical solvers and floating-point computations. CPP 2017 Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs, p. 90-99, 2017.

• J. Modayil. Discovering Sensor Space: Constructing Spatial Embeddings That Explain Sensor Correlations. 9th International Conference on Development and Learning, 120-125, 2010.

• E. Möhlmann and O. Theel. Stabhyli: a tool for automatic stability verification of non-linear hybrid systems. HSCC '13 Proceedings of the 16th International Conference on Hybrid Systems: Computation and Control, pages 107-112, 2013.

• E. Möhlmann, W. Hagemann, O. Theel. Hybrid Tools for Hybrid Systems – Proving Stability and Safety at Once. In: Sankaranarayanan S., Vicario E. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2015. Lecture Notes in Computer Science, vol 9268. Springer, 2015.

• R. Muminovic, N. Werner, J. Pfeiffer, and R. King. Drag Reduction of Two 2-D Bluff Bodies in a Tandem Arrangement Through Robust Model Predictive Control. 5th Flow Control Conference, 2010.

• K. Nakahira and K. Kato. Simple Upper and Lower Bounds on the Ultimate Success Probability for Discriminating Arbitrary Finite-Dimensional Quantum Processes. Physical Review Letters 126:200502, 2021.

• F. Nan, M. Moghadasi, P. Vakili, S. Vaqjda, D. Kozakov, and I. Ch. Paschalidis. A Subspace Semi-definite Programming-Based Underestimation (SSDU) Method for Stochastic Global Optimization in Protein Docking. 53rd IEEE Conference on Decision and Control, 4623-4628, 2014.

• J. Neto and W. Ben-Ameur. On Fractional Cut Covers. Discrete Applied Mathematics, 265:168-181, 2019.

• I. Nowak. A New Semidefinite Programming Bound for Indefinite Quadratic Forms Over a Simplex. Journal of Global Optimization 14(4):357-364, 1999.

• J. Oehlerking, H. Burchardt, and O. Theel. Towards Automatic Verification of Affine Hybrid System Stability. ACM SIGBED Review 2(2):27-30, 2005. Preprint.

• S. Oliveira, D. Stewart, and T. Soma. A Subspace Semidefinite Programming for Spectral Graph Partitioning. In Computational Science - ICCS 2002. Lecture Notes in Computer Science 2329:1058-1067, 2002.

• M. K. Omar, J. Pelecanos, and G. N. Ramaswamy. Maximum Margin Linear Kernel Optimization for Speaker Verification. International Conference on Acoustics, Speech, and Signal Processing, 4037-4040, 2009.

• P. V. Pakshin and S. G. Soloviev. SCIYALMIP: a free tool for solution to semidefinite programming problems in SCILAB. IFAC Proceedings Volumes, 8th IFAC Symposium on Advances in Control Education 42, 245–249, 2009.

• K. F. Pal and T. Vertesi. Quantum Bounds on Bell Inequalities. Physical Review A 79 022120, 2009.

• K. F. Pal and T. Vertesi. Maximal violation of a bipartite three-setting, two-outcome Bell inequality using infinite-dimensional quantum systems. Physical Review A 82 022116, 2010.

• D. Papp. Semi-Infinite Programming using High-Degree Polynomial Interpolants and Semidefinite Programming. SIAM Journal on Optimization 27(3):1858–1879, 2017.

• A. A. Pessoa and M. Poss. Robust Network Design with Uncertain Outsourcing Cost. INFORMS Journal on Computing, 27:507-524, 2015.

• M. C. Plateau and Y. A. Rios-Solis. Optimal solutions for unrelated parallel machines scheduling problems using convex quadratic reformulations. European Journal of Operational Research 201(3):729-736, 2010. Preprint.

• A. Platzer, J. D. Quessel, and P. Rummer. Real World Verification. In Automated Deduction – CADE-22, Lecture Notes in Computer Science, vol. 5663, pages 485-501, Springer, 2009.

• M. F. Pusey. Negativity and Steering: A Stronger Peres Conjecture. Physical Review A, 88:032313, 2013.

• A. Razborov. Flag Algebras. Journal of Symbolic Logic 72(4):1239-1282, 2007. Preprint.

• A. Razborov. On 3-Hypergraphs with Forbidden 4-Vertex Configurations. SIAM Journal on Discrete Mathematics 24(3):946-963, 2010.

• A. Razborov. Flag Algebras: An Interim Report. In "The Mathematics of Paul Erdős II", pages 207-232, 2013.

• P. Roux and P. Garoche. Integrating Policy Iterations in Abstract Interpreters. Automated Technology for Verification and Analysis. Lecture Notes in Computer Science Volume 8172:240-254, 2013.

• P. Roux, M. Iguernlal, and S. Conchon. A Non-Linear Arithmetic Procedure for Control-Command Software Verification. In Tools and Algorithms for the Construction and Analysis of Systems, 132–51. Lecture Notes in Computer Science. Springer, 2018.

• C. Schellewald. A Convex Relaxation Bound for Subgraph Isomorphism. International Journal of Combinatorics, Article ID 908356, 2012.

• F. Shang, L. C. Jiao, Y. Liu, and F. Wang. Learning Spectral Embedding via Iterative Eigenvalue Thresholding. CIKM '12 Proceedings of the 21st ACM International Conference on Information and Knowledge Management. 1507-1511, 2012.

• Y. Shavitt and T. Tankel. Big-Bang Simulation for Embedding Network Distances in Euclidean Space. IEEE/ACM Transactions on Networking 12(6):993-1006, 2004. Preprint.

• C. Shen, H. Li, and M. J. Brooks. Supervised Dimensionality Reduction Via Sequential Semidefinite Programming. Pattern Recognition, 41:3644-3652, 2008.

• J. Shao and G. Rong. Nonlinear Process Monitoring Based on Maximum Variance Unfolding Projections. Expert Systems with Applications 36:11332-11340, 2009.

• K. K. Sivaramakrishnan. A parallel interior point decomposition algorithm for block angular semidefinite programs. Computational Optimization and Applications 46(1):1-29, 2010.

• B. Song and V. Li. A Hybridization between Memetic Algorithm and Semidefinite Relaxation for the Max-Cut Problem. GECCO '12 Proceedings of the fourteenth international conference on Genetic and evolutionary computation conference, page 425-432, 2012.

• N. Srebro, J. D. M. Rennie, and T. S. Jaakkola. Maximum-Margin Matrix Factorization. In Advances in Neural Information Processing Systems 17, Proceedings of the 2004 Conference. Edited by Lawrence K. Saul, Yair Weiss and Léon Bottou. pages 1329-1336, 2005.

• S. Szabo and B. Zavalnij. Estimating Clique Size via Discarding Subgraphs. Informatica 45:197-204, 2021.

• P. L. Takouda, M. F. Anjos, and A. Vannelli. Global Lower Bounds for the VLSI Macrocell Floorplanning Problem using Semidefinite Optimization. In Proceedings. Fifth International Workshop on System-on-Chip for Real-Time Applications, pages 275-280, 2005.

• C. Tantipathananandh and T. Y. Berger-Wolf. Finding Communities in Dynamic Social Networks. 11th IEEE International Conference on Data Mining, 1236-1241, 2011.

• I. Tziakos, A. Cavallaro, and L. Q. Xu. Video Event Segmentation and Visualisation in Non-linear Subspace. Pattern Recognition Letters 30:123-131, 2009.

• T. Vértesi and K. F. Pál. Nonclassicality threshold for the three-qubit Greenberger-Horne-Zeilinger state. Physical Review A 84, 042122, 2011.

• X. Wang, X. Wang, Z. Wang, and F. Qian. A novel method for detecting processes with multi-state modes. Control Engineering Practice 21:1788-1794, 2013.

• Z. Wang and X. Sun. Multiple kernel local Fisher discriminant analysis for face recognition. Signal Processing 93:1496-1509, 2013.

• Z. Wang, X. Sun, L. Sun, and Y. Huang. Semisupervised Kernel Marginal Fisher Analysis for Face Recognition. The Scientific World Journal. 981840, 2013.

• C. Wei, J. Chen, and Z. Song. Developments of Two Supervised Maximum Variance Unfolding Algorithms for Process Classification. Chemometrics and Intelligent Laboratory Systems 159:31-44, 2016.

• C. Wei, J. Chen, and Z. Song. Multilevel MVU models with localized construction for monitoring processes with large scale data . Journal of Process Control 67:176-196, 2018.

• C. Wei, J. Chen, Z. Song, and C. I. Chen. Soft Sensors of Nonlinear Industrial Processes Based on Self-Learning Kernel Regression Model. In 2017 11th Asian Control Conference (ASCC), 1783–88. 2017.

• K. Q. Weinberger, B. D. Packer, and L. K. Saul. Nonlinear Dimensionality Reduction by Semidefinite Programming and Kernel Matrix Factorization. In Z. Ghahramani and R. Cowell (eds.), Proceedings of the Tenth International Workshop on Artificial Intelligence and Statistics, pages 381-388, 2005.

• K. Q. Weinberger and L. K. Saul. Unsupervised Learning of Image Manifolds by Semidefinite Programming. International Journal of Computer Vision 70(1):77-90, 2006. Preprint.

• R. Wellman. Optimum Contribution Selection for Animal Breeding and Conservation: The R Package OptiSel. BMC Bioinformatics 20:25, 2019.

• C. W. Wu. On a Matrix Inequality and its Application to the Synchronization in Coupled Chaotic Systems. In İ. C. Göknar and L. Sevgi (eds.), Complex Computing-Networks, Springer Proceedings in Physics Volume 104, Springer, pages 279-287, 2006.

• B. Xue, Z. She, and A. Easwaran. Underapproximating Backward Reachable Sets by Semialgebraic Sets. IEEE Transactions on Automatic Control 62(10):5185-5197, 2017.

• S. Yan, J. Liu, X. Tang, and T. S. Huang. Formulating Face Verification With Semidefinite Programming. IEEE Transactions on Image Processing 16(11):2802-2810, 2007.

• S. Yan, H. Wang, X. Tang, J. Liu, T. S. Huang. Regression From Uncertain Labels and its Applications to Soft Biometrics. IEEE Transactions on Information Forensics and Security 3(4):698-708, 2008.

• L. Yang, M. Wang, S. Yang, R. Zhang, and P. Zhang. Sparse Spatio-Spectral LapXVM with Semisupervised Kernel Propagation for Hyperspectral Image Classifications. IEEE Journal on Selected Topics in Applied Earth Observations and Remote Sensing 10(5):2046-2054, 2017.

• B. Yu, Y. H. Lin, G. Luk-Pat, D. Z. Pan. A High-Performance Triple Patterning Layout Decomposer with Balanced Density. In IEEE/ACM International Conference on Computer-Aided Design (ICCAD), pages 163-169, 2013.

• B. Yu and D. Z. Pan. Layout Decomposition for Quadruple Patterning Lithography and Beyond. In DAC '14 Proceedings of the 51st Annual Design Automation Conference, pages 1-6, 2014.

• B. Yu, K. Yuan, D. Ding, and D. Z. Pan. Layout Decomposition for Triple Patterning Lithography. IEEE Transactions on Computer-Aided Design of Integerated Circuits and Systems, 34(3):433-446, 2015.

• S. Zarbafian, M. Moghadasi, A. Roshandelpoor, F. Nan, K. Li, P. Vakli, S. Vajda, D. Kozakov, and I. Ch. Paschalidis. Protein Docking Refinement by Convex Underestimation in the Low-Dimensional Subspace of Encounter Complexes. Scientific Reports 8 (1): 5896, 2018.

• M. Zeng. Feynman Integrals from Positivity Constraints. _Journal of High Energy Physics _, 2023.9:1-43.

• X. Zeng. Inner Product Laplacian Embedding Based on Semidefinite Programming. Journal of Signal and Information Processing 2:196-204, 2011.

• B. Zhang, J. Yan, N. Liu, Q. Cheng, Z. Chen, and W-Y Ma. Supervised Semi-definite Embedding for Image Manifolds. IEEE International Conference on Multimedia and Expo, 2005.