SNOPT: An SQP algorithm for large-scale constrained optimization. Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available and that the constraint gradients are sparse. We discuss an SQP algorithm that uses a smooth augmented Lagrangian merit function and makes explicit provision for infeasibility in the original problem and the QP subproblems. SNOPT is a particular implementation that makes use of a semidefinite QP solver. It is based on a limited-memory quasi-Newton approximation to the Hessian of the Lagrangian and uses a reduced-Hessian algorithm (SQOPT) for solving the QP subproblems. It is designed for problems with many thousands of constraints and variables but a moderate number of degrees of freedom (say, up to 2000). An important application is to trajectory optimization in the aerospace industry. Numerical results are given for most problems in the CUTE and COPS test collections (about 900 examples).

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  1. Araya, Ignacio; Reyes, Victor: Interval branch-and-bound algorithms for optimization and constraint satisfaction: a survey and prospects (2016)
  2. Betts, John T.; Campbell, Stephen L.; Thompson, Karmethia C.: Solving optimal control problems with control delays using direct transcription (2016)
  3. Bolte, Jér^ome; Pauwels, Edouard: Majorization-minimization procedures and convergence of SQP methods for semi-algebraic and tame programs (2016)
  4. Burdakov, Oleg P.; Kanzow, Christian; Schwartz, Alexandra: Mathematical programs with cardinality constraints: reformulation by complementarity-type conditions and a regularization method (2016)
  5. Cannataro, Begüm Şenses; Rao, Anil V.; Davis, Timothy A.: State-defect constraint pairing graph coarsening method for Karush-Kuhn-Tucker matrices arising in orthogonal collocation methods for optimal control (2016)
  6. Foraker, Joseph; Royset, Johannes O.; Kaminer, Isaac: Search-trajectory optimization. II: Algorithms and computations (2016)
  7. Forsgren, Anders; Gill, Philip E.; Wong, Elizabeth: Primal and dual active-set methods for convex quadratic programming (2016)
  8. Guzman, Yannis A.; Faruque Hasan, M.M.; Floudas, Christodoulos A.: Performance of convex underestimators in a branch-and-bound framework (2016)
  9. Houska, Boris; Frasch, Janick; Diehl, Moritz: An augmented Lagrangian based algorithm for distributed nonconvex optimization (2016)
  10. Izmailov, A.F.; Solodov, M.V.; Uskov, E.I.: Globalizing stabilized sequential quadratic programming method by smooth primal-dual exact penalty function (2016)
  11. Kočvara, Michal; Mohammed, Sudaba: Primal-dual interior point multigrid method for topology optimization (2016)
  12. Phelps, Chris; Royset, Johannes O.; Gong, Qi: Optimal control of uncertain systems using sample average approximations (2016)
  13. Shen, Chungen; Zhang, Lei-Hong; Liu, Wei: A stabilized filter SQP algorithm for nonlinear programming (2016)
  14. Shen, Chungen; Zhang, Lei-Hong; Yang, Wei Hong: A filter active-set algorithm for ball/sphere constrained optimization problem (2016)
  15. Valentin, Julian; Pflüger, Dirk: Hierarchical gradient-based optimization with B-splines on sparse grids (2016)
  16. Yoda, Kunikazu; Prékopa, András: Convexity and solutions of stochastic multidimensional 0-1 knapsack problems with probabilistic constraints (2016)
  17. Zhu, Xiaojing: On a globally convergent trust region algorithm with infeasibility control for equality constrained optimization (2016)
  18. Arioli, Mario; Duff, Iain S.: Preconditioning linear least-squares problems by identifying a basis matrix (2015)
  19. Bao, Xiaowei; Khajavirad, Aida; Sahinidis, Nikolaos V.; Tawarmalani, Mohit: Global optimization of nonconvex problems with multilinear intermediates (2015)
  20. Bremer, I.; Henrion, R.; Möller, A.: Probabilistic constraints via SQP solver: application to a renewable energy management problem (2015)

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