SQPlab
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)
Keywords for this software
References in zbMATH (referenced in 145 articles , 1 standard article )
Showing results 1 to 20 of 145.
Sorted by year (- 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)
- Chrétien, Stéphane; Clarkson, Paul: A fast algorithm for the semi-definite relaxation of the state estimation problem in power grids (2020)
- Deng, Hao; Hinnebusch, Shawn; To, Albert C.: Topology optimization design of stretchable metamaterials with Bézier skeleton explicit density (BSED) representation algorithm (2020)
- Finardi, E. C.; Lobato, R. D.; de Matos, V. L.; Sagastizábal, C.; Tomasgard, A.: Stochastic hydro-thermal unit commitment via multi-level scenario trees and bundle regularization (2020)
- Gdawiec, Krzysztof; Shahid, Abdul Aziz; Nazeer, Waqas: Higher order methods of the basic family of iterations via (S)-iteration scheme with (s)-convexity (2020)
- Hare, Warren; Planiden, Chayne; Sagastizábal, Claudia: A derivative-free (\mathcalV\mathcalU)-algorithm for convex finite-max problems (2020)
- Helou, Elias S.; Santos, Sandra A.; Simões, Lucas E. A.: A new sequential optimality condition for constrained nonsmooth optimization (2020)
- Ito, Kazufumi: Value function calculus and applications (2020)
- Luna, Juan Pablo; Sagastizábal, Claudia; Solodov, Mikhail: A class of Benders decomposition methods for variational inequalities (2020)
- Mitridati, Lesia; Kazempour, Jalal; Pinson, Pierre: Heat and electricity market coordination: a scalable complementarity approach (2020)
- Pang, Li-Ping; Wu, Qi; Wang, Jin-He; Wu, Qiong: A discretization algorithm for nonsmooth convex semi-infinite programming problems based on bundle methods (2020)
- Pay, Babak Saleck; Song, Yongjia: Partition-based decomposition algorithms for two-stage stochastic integer programs with continuous recourse (2020)
- Tang, Chunming; Liu, Shuai; Jian, Jinbao; Ou, Xiaomei: A multi-step doubly stabilized bundle method for nonsmooth convex optimization (2020)
- Theljani, Anis; Chen, Ke: A Nash game based variational model for joint image intensity correction and registration to deal with varying illumination (2020)
- de Oliveira, Welington: Proximal bundle methods for nonsmooth DC programming (2019)
- Dussault, Jean-Pierre; Frappier, Mathieu; Gilbert, Jean Charles: A lower bound on the iterative complexity of the Harker and Pang globalization technique of the Newton-min algorithm for solving the linear complementarity problem (2019)
- Effio Saldivar, Carolina; Herskovits, José; Luna, Juan Pablo; Sagastizábal, Claudia: Multidimensional calibration of crude oil and refined products via semidefinite programming techniques (2019)
- Ellabib, Abdellatif; Ouakrim, Youssef: A vectorized regularization method for multivalued parameters identification (2019)
- Ellabib, Abdellatif; Ouakrim, Youssef: Inverse problem for a class of nonlinear elliptic equations with entropy solution (2019)
- Erhel, Jocelyne; Migot, Tangi: Characterizations of solutions in geochemistry: existence, uniqueness, and precipitation diagram (2019)