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 102 articles , 1 standard article )

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  1. Bolte, Jér^ome; Hochart, Antoine; Pauwels, Edouard: Qualification conditions in semialgebraic programming (2018)
  2. Delfino, A.; de Oliveira, W.: Outer-approximation algorithms for nonsmooth convex MINLP problems (2018)
  3. Hare, W.; Planiden, C.: Computing proximal points of convex functions with inexact subgradients (2018)
  4. Jian, Jin-bao; Tang, Chun-ming; Shi, Lu: A feasible point method with bundle modification for nonsmooth convex constrained optimization (2018)
  5. Kolosnitsyn, A. V.: Computational efficiency of the simplex embedding method in convex nondifferentiable optimization (2018)
  6. Bajaj, Anuj; Hare, Warren; Lucet, Yves: Visualization of the $\varepsilon $-subdifferential of piecewise linear-quadratic functions (2017)
  7. Bonnans, J. Frédéric; Festa, Adriano: Error estimates for the Euler discretization of an optimal control problem with first-order state constraints (2017)
  8. Carlier, Guillaume; Dupuis, Xavier: An iterated projection approach to variational problems under generalized convexity constraints (2017)
  9. Gilbert, Jean Charles: On the solution uniqueness characterization in the L1 norm and polyhedral gauge recovery (2017)
  10. Helou, Elias Salomão; Santos, Sandra A.; Simões, Lucas E. A.: On the local convergence analysis of the gradient sampling method for finite max-functions (2017)
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  14. Shen, W. P.; Li, C.; Yao, J. C.: Approximate Cayley transform methods for inverse eigenvalue problems and convergence analysis (2017)
  15. Shi, Y.; Tuan, H. D.; Tuy, H.; Su, S.: Global optimization for optimal power flow over transmission networks (2017)
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  17. Tong, Jun; Hu, Jian-Qiang; Hu, Jiaqiao: A computational algorithm for equilibrium asset pricing under heterogeneous information and short-sale constraints (2017)
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  19. van Ackooij, Wim: A comparison of four approaches from stochastic programming for large-scale unit-commitment (2017)
  20. Xue, Yuan; Zhang, Nan; Yin, Xiangrong; Zheng, Haitao: Sufficient dimension reduction using Hilbert-Schmidt independence criterion (2017)

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