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.

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  1. Cavaleiro, Marta; Alizadeh, Farid: A dual simplex-type algorithm for the smallest enclosing ball of balls (2021)
  2. Cheng, Sheng; Martins, Nuno C.: An optimality gap test for a semidefinite relaxation of a quadratic program with two quadratic constraints (2021)
  3. Chen, Zhongzhu; Fampa, Marcia; Lambert, Amélie; Lee, Jon: Mixing convex-optimization bounds for maximum-entropy sampling (2021)
  4. Dickinson, Peter J. C.; de Zeeuw, Reinier: Generating irreducible copositive matrices using the stable set problem (2021)
  5. Ding, Xiaodong; Luo, Hezhi; Wu, Huixian; Liu, Jianzhen: An efficient global algorithm for worst-case linear optimization under uncertainties based on nonlinear semidefinite relaxation (2021)
  6. Ferrante, Francesco; Prieur, Christophe: Boundary control design for conservation laws in the presence of measurement disturbances (2021)
  7. Gillis, Nicolas; Sharma, Punit: Minimal-norm static feedbacks using dissipative Hamiltonian matrices (2021)
  8. Henrion, Didier; Naldi, Simone; Safey El Din, Mohab: Exact algorithms for semidefinite programs with degenerate feasible set (2021)
  9. Jiao, Liguo; Lee, Jae Hyoung: Finding efficient solutions in robust multiple objective optimization with SOS-convex polynomial data (2021)
  10. Liang, Ling; Sun, Defeng; Toh, Kim-Chuan: An inexact augmented Lagrangian method for second-order cone programming with applications (2021)
  11. Lin, Tianyi; Ma, Shiqian; Ye, Yinyu; Zhang, Shuzhong: An ADMM-based interior-point method for large-scale linear programming (2021)
  12. Lourenço, Bruno F.; Muramatsu, Masakazu; Tsuchiya, Takashi: Solving SDP completely with an interior point oracle (2021)
  13. Luo, Hezhi; Ding, Xiaodong; Peng, Jiming; Jiang, Rujun; Li, Duan: Complexity results and effective algorithms for worst-case linear optimization under uncertainties (2021)
  14. Ma, Weiwei; Jia, Xin-Chun; Chi, Xiaobo: Exponential stabilization of sampled-data fuzzy systems via a parameterized fuzzy Lyapunov-Krasovskii functional approach (2021)
  15. Mishra, Prabhat K.; Diwale, Sanket S.; Jones, Colin N.; Chatterjee, Debasish: Reference tracking stochastic model predictive control over unreliable channels and bounded control actions (2021)
  16. Naldi, Simone; Sinn, Rainer: Conic programming: infeasibility certificates and projective geometry (2021)
  17. Padmanabhan, Divya; Natarajan, Karthik; Murthy, Karthyek: Exploiting partial correlations in distributionally robust optimization (2021)
  18. Polyak, B. T.; Khlebnikov, M. V.; Shcherbakov, P. S.: Linear matrix inequalities in control systems with uncertainty (2021)
  19. Santoyo, Cesar; Dutreix, Maxence; Coogan, Samuel: A barrier function approach to finite-time stochastic system verification and control (2021)
  20. Shen, Chungen; Wang, Yunlong; Xue, Wenjuan; Zhang, Lei-Hong: An accelerated active-set algorithm for a quadratic semidefinite program with general constraints (2021)

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