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. Church, Richard L.; Drezner, Zvi: Review of obnoxious facilities location problems (2022)
  2. Gorissen, Bram L.: Interior point methods can exploit structure of convex piecewise linear functions with application in radiation therapy (2022)
  3. Kalczynski, Pawel; Drezner, Zvi: Extremely non-convex optimization problems: the case of the multiple obnoxious facilities location (2022)
  4. Kirches, Christian; Larson, Jeffrey; Leyffer, Sven; Manns, Paul: Sequential linearization method for bound-constrained mathematical programs with complementarity constraints (2022)
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  6. Pager, Elisha R.; Rao, Anil V.: Method for solving bang-bang and singular optimal control problems using adaptive Radau collocation (2022)
  7. Bakhta, Athmane; Vidal, Julien: Modeling and optimization of the fabrication process of thin-film solar cells by multi-source physical vapor deposition (2021)
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  10. Deptula, Patryk; Bell, Zachary I.; Zegers, Federico M.; Licitra, Ryan A.; Dixon, Warren E.: Approximate optimal influence over an agent through an uncertain interaction dynamic (2021)
  11. Ding Ma, Dominique Orban, Michael A. Saunders: A Julia implementation of Algorithm NCL for constrained optimization (2021) arXiv
  12. Drezner, Tammy; Drezner, Zvi; Kalczynski, Pawel: Directional approach to gradual cover: the continuous case (2021)
  13. Eide, Joseph D.; Hager, William W.; Rao, Anil V.: Modified Legendre-Gauss-Radau collocation method for optimal control problems with nonsmooth solutions (2021)
  14. Gabriel, Steven A.; Leal, Marina; Schmidt, Martin: Solving binary-constrained mixed complementarity problems using continuous reformulations (2021)
  15. Ghantasala, Aditya; Najian Asl, Reza; Geiser, Armin; Brodie, Andrew; Papoutsis, Efthymios; Bletzinger, Kai-Uwe: Realization of a framework for simulation-based large-scale shape optimization using vertex morphing (2021)
  16. Hermans, Ben; Pipeleers, Goele; Patrinos, Panagiotis (Panos): A penalty method for nonlinear programs with set exclusion constraints (2021)
  17. Horowitz, Joel L.; Nesheim, Lars: Using penalized likelihood to select parameters in a random coefficients multinomial logit model (2021)
  18. Jones, Morgan; Peet, Matthew M.: A generalization of Bellman’s equation with application to path planning, obstacle avoidance and invariant set estimation (2021)
  19. Kalczynski, Pawel; Drezner, Zvi: The obnoxious facilities planar (p)-median problem (2021)
  20. Krulikovski, Evelin H. M.; Ribeiro, Ademir A.; Sachine, Mael: On the weak stationarity conditions for mathematical programs with cardinality constraints: a unified approach (2021)

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