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. Bock, Hans Georg; Kirches, Christian; Meyer, Andreas; Potschka, Andreas: Numerical solution of optimal control problems with explicit and implicit switches (2018)
  2. 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)
  3. Duarte, Belmiro P. M.; Wong, Weng Kee; Dette, Holger: Adaptive grid semidefinite programming for finding optimal designs (2018)
  4. 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)
  5. Kılınç, Mustafa R.; Sahinidis, Nikolaos V.: Exploiting integrality in the global optimization of mixed-integer nonlinear programming problems with BARON (2018)
  6. Ledoit, Olivier; Wolf, Michael: Optimal estimation of a large-dimensional covariance matrix under Stein’s loss (2018)
  7. Putkaradze, Vakhtang; Rogers, Stuart: Constraint control of nonholonomic mechanical systems (2018)
  8. Semmler, Johannes; Pflug, Lukas; Stingl, Michael: Material optimization in transverse electromagnetic scattering applications (2018)
  9. Shi-Dong, Doug; Nadarajah, Siva: Approximate Hessian for accelerated convergence of aerodynamic shape optimization problems in an adjoint-based framework (2018)
  10. Torrisi, Giampaolo; Grammatico, Sergio; Smith, Roy S.; Morari, Manfred: A projected gradient and constraint linearization method for nonlinear model predictive control (2018)
  11. Alipour, Khalil; Daemi, Parisa; Hassanpour, Arman; Tarvirdizadeh, Bahram: On the capability of wheeled mobile robots for heavy object manipulation considering dynamic stability constraints (2017)
  12. Armand, Paul; Omheni, Riadh: A mixed logarithmic barrier-augmented Lagrangian method for nonlinear optimization (2017)
  13. Curtis, Frank E.; Gould, Nicholas I. M.; Robinson, Daniel P.; Toint, Philippe L.: An interior-point trust-funnel algorithm for nonlinear optimization (2017)
  14. Fan, Jinyan; Zhou, Anwa: A semidefinite algorithm for completely positive tensor decomposition (2017)
  15. Hansen, Pierre; Mladenović, Nenad; Todosijević, Raca; Hanafi, Saïd: Variable neighborhood search: basics and variants (2017)
  16. Jian, Jinbao; Zeng, Hanjun; Ma, Guodong; Zhu, Zhibin: Primal-dual interior point QP-free algorithm for nonlinear constrained optimization (2017)
  17. Kaya, C. Yalçın: Markov-Dubins path via optimal control theory (2017)
  18. Kelly, Matthew: An introduction to trajectory optimization: how to do your own direct collocation (2017)
  19. Khan, Kamil A.; Watson, Harry A. J.; Barton, Paul I.: Differentiable McCormick relaxations (2017)
  20. Mummolo, Carlotta; Mangialardi, Luigi; Kim, Joo H.: Numerical estimation of balanced and falling states for constrained legged systems (2017)

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