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. Drezner, Tammy; Drezner, Zvi; Kalczynski, Pawel: The planar multifacility collection depots location problem (2019)
  2. Amaya Moreno, Liana; Fügenschuh, Armin; Kaier, Anton; Schlobach, Swen: A nonlinear model for vertical free-flight trajectory planning (2018)
  3. Bock, Hans Georg; Kirches, Christian; Meyer, Andreas; Potschka, Andreas: Numerical solution of optimal control problems with explicit and implicit switches (2018)
  4. Branda, Martin; Bucher, Max; Červinka, Michal; Schwartz, Alexandra: Convergence of a Scholtes-type regularization method for cardinality-constrained optimization problems with an application in sparse robust portfolio optimization (2018)
  5. Dalkiran, Evrim; Ghalami, Laleh: On linear programming relaxations for solving polynomial programming problems (2018)
  6. Duarte, Belmiro P. M.; Sagnol, Guillaume; Wong, Weng Kee: An algorithm based on semidefinite programming for finding minimax optimal designs (2018)
  7. Duarte, Belmiro P. M.; Wong, Weng Kee; Dette, Holger: Adaptive grid semidefinite programming for finding optimal designs (2018)
  8. Ge, Xinsheng; Yao, Qijia; Chen, Liqun: Control strategy of optimal deployment for spacecraft solar array system with initial state uncertainty (2018)
  9. Helou, Elias S.; Santos, Sandra A.; Simões, Lucas E. A.: A fast gradient and function sampling method for finite-max functions (2018)
  10. He, Ping; Mader, Charles A.; Martins, Joaquim R. R. A.; Maki, Kevin J.: An aerodynamic design optimization framework using a discrete adjoint approach with OpenFOAM (2018)
  11. Khajavirad, Aida; Sahinidis, Nikolaos V.: A hybrid LP/NLP paradigm for global optimization relaxations (2018)
  12. Kılınç, Mustafa R.; Sahinidis, Nikolaos V.: Exploiting integrality in the global optimization of mixed-integer nonlinear programming problems with BARON (2018)
  13. Ledoit, Olivier; Wolf, Michael: Optimal estimation of a large-dimensional covariance matrix under Stein’s loss (2018)
  14. Pei, Yong Gang; Zhu, De Tong: On the global convergence of a projective trust region algorithm for nonlinear equality constrained optimization (2018)
  15. Putkaradze, Vakhtang; Rogers, Stuart: Constraint control of nonholonomic mechanical systems (2018)
  16. Ribeiro, Ademir A.; Sachine, Mael; Santos, Sandra A.: On the approximate solutions of augmented subproblems within sequential methods for nonlinear programming (2018)
  17. Schmitt, Oliver; Steinmann, Paul: Control of minimum member size in parameter-free structural shape optimization by a medial axis approximation (2018)
  18. Semmler, Johannes; Pflug, Lukas; Stingl, Michael: Material optimization in transverse electromagnetic scattering applications (2018)
  19. Sequeira, Adélia; Tiago, Jorge; Guerra, Telma: Boundary control problems in hemodynamics (2018)
  20. Shi-Dong, Doug; Nadarajah, Siva: Approximate Hessian for accelerated convergence of aerodynamic shape optimization problems in an adjoint-based framework (2018)

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