SDPT3

This software is designed to solve conic programming problems whose constraint cone is a product of semidefinite cones, second-order cones, nonnegative orthants and Euclidean spaces; and whose objective function is the sum of linear functions and log-barrier terms associated with the constraint cones. This includes the special case of determinant maximization problems with linear matrix inequalities. It employs an infeasible primal-dual predictor-corrector path-following method, with either the HKM or the NT search direction. The basic code is written in Matlab, but key subroutines in C are incorporated via Mex files. Routines are provided to read in problems in either SDPA or SeDuMi format. Sparsity and block diagonal structure are exploited. We also exploit low-rank structures in the constraint matrices associated the semidefinite blocks if such structures are explicitly given. To help the users in using our software, we also include some examples to illustrate the coding of problem data for our SQLP solver. Various techniques to improve the efficiency and stability of the algorithm are incorporated. For example, step-lengths associated with semidefinite cones are calculated via the Lanczos method. Numerical experiments show that this general purpose code can solve more than 80% of a total of about 300 test problems to an accuracy of at least 10−6 in relative duality gap and infeasibilities.


References in zbMATH (referenced in 444 articles , 1 standard article )

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  1. Kaiser, Eurika; Morzyński, Marek; Daviller, Guillaume; Kutz, J.Nathan; Brunton, Bingni W.; Brunton, Steven L.: Sparsity enabled cluster reduced-order models for control (2018)
  2. Abou Jaoude, Dany; Farhood, Mazen: Distributed control of nonstationary LPV systems over arbitrary graphs (2017)
  3. Abou Jaoude, Dany; Farhood, Mazen: Balanced truncation model reduction of nonstationary systems interconnected over arbitrary graphs (2017)
  4. Arima, Naohiko; Kim, Sunyoung; Kojima, Masakazu; Toh, Kim-Chuan: A robust Lagrangian-DNN method for a class of quadratic optimization problems (2017)
  5. Briat, Corentin: Dwell-time stability and stabilization conditions for linear positive impulsive and switched systems (2017)
  6. Cifuentes, Diego; Parrilo, Pablo A.: Sampling algebraic varieties for sum of squares programs (2017)
  7. Ding, Chao; Qi, Hou-Duo: Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation (2017)
  8. Ding, Chao; Qi, Hou-Duo: Convex optimization learning of faithful Euclidean distance representations in nonlinear dimensionality reduction (2017)
  9. Ducuara, Andrés F.; Susa, Cristian E.; Reina, John H.: Not-Post-Peierls compatibility under noisy channels (2017)
  10. Dumitrescu, Bogdan: Positive trigonometric polynomials and signal processing applications (2017)
  11. Fendl, Hannes; Neumaier, Arnold; Schichl, Hermann: Certificates of infeasibility via nonsmooth optimization (2017)
  12. Ge, Ming; Kerrigan, Eric C.: Noise covariance identification for nonlinear systems using expectation maximization and moving horizon estimation (2017)
  13. Gillis, Nicolas; Sharma, Punit: On computing the distance to stability for matrices using linear dissipative Hamiltonian systems (2017)
  14. Hand, Paul: Phaselift is robust to a constant fraction of arbitrary errors (2017)
  15. Huang, Wen; Gallivan, K.A.; Zhang, Xiangxiong: Solving phaselift by low-rank Riemannian optimization methods for complex semidefinite constraints (2017)
  16. Hu, Bin; Lacerda, Márcio J.; Seiler, Peter: Robustness analysis of uncertain discrete-time systems with dissipation inequalities and integral quadratic constraints (2017)
  17. Kuti, József; Galambos, Péter; Baranyi, Péter: Minimal volume simplex (MVS) polytopic model generation and manipulation methodology for TP model transformation (2017)
  18. Lasserre, Jean B.; Toh, Kim-Chuan; Yang, Shouguang: A bounded degree SOS hierarchy for polynomial optimization (2017)
  19. Mao, Qi; Wang, Li; Tsang, Ivor W.: A unified probabilistic framework for robust manifold learning and embedding (2017)
  20. Mohammad-Nezhad, Ali; Terlaky, Tamás: A polynomial primal-dual affine scaling algorithm for symmetric conic optimization (2017)

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