The SQPlab (pronounce S-Q-P-lab) software presented in these pages is a modest Matlab implementation of the SQP algorithm for solving constrained optimization problems. The functions defining the problem can be nonlinear and nonconvex, but must be differentiable. A particular attention will be paid to problems with an optimal control structure. SQP stands for Sequential Quadratic Programming, a method invented in the mid-seventies, which can be viewed as the Newton approach applied to the optimality conditions of the optimization problem. Each iteration of the SQP algorithm requires finding a solution to a quadratic program (QP). This is a simpler optimization problem, which has a quadratic objective and linear constraints. This QP is still difficult to solve however; in particular it is NP-hard when the quadratic objective is nonconvex. On the other hand, as a Newton method, the SQP algorithm converges very rapidly, meaning that it requires few iterations (hence QP solves) to find an approximate solution with a good precision (this is particularly true when second derivatives are used). Therefore, one can say that the SQP algorithm is an appropriate approach when the evaluation of the functions defining the nonlinear optimization problem, and their derivatives, is time consuming. Indeed, in this case, the time spent in finding the solution to the QP’s is counterbalanced by the time spent in evaluating nonlinear functions. Since the functions are evaluated once at each iteration, one can then benefit from the small number of iterations required by the method. If the rule above does not apply, a nonlinear interior point algorithm can do better. (Source: http://plato.asu.edu)

References in zbMATH (referenced in 175 articles , 1 standard article )

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  1. Kouri, Drew P.; Surowiec, Thomas M.: A primal-dual algorithm for risk minimization (2022)
  2. Sarabi, M. Ebrahim: Primal superlinear convergence of SQP methods in piecewise linear-quadratic composite optimization (2022)
  3. Steakelum, Joshua; Aubertine, Jacob; Chen, Kenan; Nagaraju, Vidhyashree; Fiondella, Lance: Multi-phase algorithm design for accurate and efficient model fitting (2022)
  4. Borges, Pedro; Sagastizábal, Claudia; Solodov, Mikhail: A regularized smoothing method for fully parameterized convex problems with applications to convex and nonconvex two-stage stochastic programming (2021)
  5. Dabaghi, Jad; Delay, Guillaume: A unified framework for high-order numerical discretizations of variational inequalities (2021)
  6. de Oliveira, Welington: Risk-averse stochastic programming and distributionally robust optimization via operator splitting (2021)
  7. Duc Thach Son Vu; Ben Gharbia, Ibtihel; Haddou, Mounir; Quang Huy Tran: A new approach for solving nonlinear algebraic systems with complementarity conditions. Application to compositional multiphase equilibrium problems (2021)
  8. El Yazidi, Youness; Ellabib, Abdellatif; Ouakrim, Youssef: On the stabilization of singular identification problem of an unknown discontinuous diffusion parameter in elliptic equation (2021)
  9. Glasner, Karl: Optimization algorithms for parameter identification in parabolic partial differential equations (2021)
  10. Harada, Kouhei: A feasibility-ensured Lagrangian heuristic for general decomposable problems (2021)
  11. Izmailov, A. F.: Accelerating convergence of a globalized sequential quadratic programming method to critical Lagrange multipliers (2021)
  12. Kuo, Yueh-Cheng; Lin, Wen-Wei; Yueh, Mei-Heng; Yau, Shing-Tung: Convergent conformal energy minimization for the computation of disk parameterizations (2021)
  13. Orlov, A. V.: On solving bilevel optimization problems with a nonconvex lower level: the case of a bimatrix game (2021)
  14. Pessia, Alberto; Tang, Jing: A three-term recurrence relation for accurate evaluation of transition probabilities of the simple birth-and-death process (2021)
  15. Yin, Jiang-hua; Jian, Jin-bao; Jiang, Xian-zhen: A generalized hybrid CGPM-based algorithm for solving large-scale convex constrained equations with applications to image restoration (2021)
  16. Almeida Guimarães, Dilson; Salles da Cunha, Alexandre; Pereira, Dilson Lucas: Semidefinite programming lower bounds and branch-and-bound algorithms for the quadratic minimum spanning tree problem (2020)
  17. Chouzenoux, Emilie; Corbineau, Marie-Caroline; Pesquet, Jean-Christophe: A proximal interior point algorithm with applications to image processing (2020)
  18. Chrétien, Stéphane; Clarkson, Paul: A fast algorithm for the semi-definite relaxation of the state estimation problem in power grids (2020)
  19. Dabaghi, Jad; Martin, Vincent; Vohralík, Martin: A posteriori estimates distinguishing the error components and adaptive stopping criteria for numerical approximations of parabolic variational inequalities (2020)
  20. Deng, Hao; Hinnebusch, Shawn; To, Albert C.: Topology optimization design of stretchable metamaterials with Bézier skeleton explicit density (BSED) representation algorithm (2020)

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