## SQPlab

 swMATH ID: 5161 Software Authors: J.F. Bonnans, J.Ch. Gilbert, C. Lemaréchal, C.A. Sagastizábal Description: 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. Homepage: https://www-rocq.inria.fr/~gilbert/modulopt/optimization-routines/sqplab/sqplab.html Programming Languages: Matlab Dependencies: Matlab Keywords: optimization; The Constrained NLO Problem Related Software: PLCP; GradSamp; Ipopt; Matlab; SNOPT; LBFGS-B; L-BFGS; LDGB; Mosek; Gurobi; CUTEr; SLQP-GS; KELLEY; PNEW; UNLocBoX; DGM; EGO; MINOS; L-BFGS-B; KNITRO Cited in: 188 Publications
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### Cited by 346 Authors

 16 Solodov, Mikhail V. 14 Sagastizábal, Claudia A. 8 de Oliveira, Welington Luis 8 Gilbert, Jean Charles 8 Izmailov, Alekseĭ F. 7 Van Ackooij, Wim 6 Jian, Jinbao 5 Tang, Chunming 4 Bonnans, Joseph Frédéric 4 Strekalovskiĭ, Aleksandr Sergeevich 3 Carlier, Guillaume 3 Ellabib, Abdellatif 3 Helou, Elias Salomão 3 Lelièvre, Tony 3 Luna, Juan Pablo 3 Orlov, Andreĭ Vasil’evich 3 Ouakrim, Youssef 3 Pang, Liping 3 Rousset, Mathias 3 Santos, Sandra Augusta 3 Schmidt, Martin 3 Simões, Lucas Eduardo Azevedo 3 Stoltz, Gabriel 2 Allaire, Grégoire 2 Apkarian, Pierre 2 Ben Gharbia, Ibtihel 2 Benmansour, Fethallah 2 Chen, Ke 2 Chouzenoux, Emilie 2 Couckuyt, Ivo 2 Dabaghi, Jad 2 Dhaene, Tom 2 Fercoq, Olivier 2 Frangioni, Antonio 2 Geers, Marc G. D. 2 Hare, Warren L. 2 Kleinert, Thomas 2 Kouri, Drew P. 2 Lacalandra, Fabrizio 2 Lanckriet, Gert R. G. 2 Lemaréchal, Claude 2 Liu, Chongyang 2 Liu, Shuai 2 Maleknia, Morteza 2 Métivier, Ludovic 2 Noll, Dominikus 2 Outrata, Jiří V. 2 Pázman, Andrej 2 Peerlings, Ron H. J. 2 Peyré, Gabriel 2 Planiden, Chayne 2 Rokoš, Ondřej 2 Santambrogio, Filippo 2 Sarabi, M. Ebrahim 2 Shamsi, Mostafa 2 Shen, Chungen 2 Shi, Ye 2 Sriperumbudur, Bharath K. 2 Surowiec, Thomas 2 Tahanan, Milad 2 Tuan, Hoang Duong 2 Turinici, Gabriel 2 Walther, Andrea 2 Wang, Xiaoliang 2 Wu, Qi 2 Yu, Bo 2 Zhang, Lei-Hong 1 Adam, Lukáš 1 Agoshkov, Valeriĭ Ivanovich 1 Alart, Pierre 1 Almeida Guimarães, Dilson 1 Alvarez-Vázquez, Lino Jose 1 Ameen, Muhsin M. 1 Ameline, Olivier 1 Amstutz, Samuel 1 An, Kaiqi 1 Armand, Paul 1 Aubertine, Jacob 1 Bajaj, Anuj 1 Baldanzini, Niccolò 1 Bardos, Claude Williams 1 Belloni, Alexandre 1 Ben-Ameur, Walid 1 Berge, V. 1 Bertsekas, Dimitri Panteli 1 Billy, Frédérique 1 Bolte, Jérôme 1 Borges, Pedro Castro 1 Borsic, A. 1 Bosse, Torsten 1 Brossier, Romain 1 Burclová, Katarína 1 Caliari, Marco 1 Cavallina, Lorenzo 1 Chauvier, Laurent 1 Chehab, Jean-Paul 1 Chen, Jein-Shan 1 Chen, Kenan 1 Chen, Wenbin 1 Chen, Zhenhua ...and 246 more Authors
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### Cited in 86 Serials

 13 Mathematical Programming. Series A. Series B 12 Computational Optimization and Applications 9 Journal of Optimization Theory and Applications 7 SIAM Journal on Optimization 7 Optimization Methods & Software 7 Set-Valued and Variational Analysis 6 Computer Methods in Applied Mechanics and Engineering 6 Optimization and Engineering 4 Journal of Computational Physics 4 Journal of Global Optimization 4 Applied Mathematical Modelling 4 European Journal of Operational Research 3 Computers & Mathematics with Applications 3 Inverse Problems 3 Mathematics and Computers in Simulation 3 Optimization 3 Annals of Operations Research 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Optimization Letters 2 Information Sciences 2 Journal of Computational and Applied Mathematics 2 Applied Numerical Mathematics 2 Computers & Operations Research 2 Asia-Pacific Journal of Operational Research 2 Computational Statistics and Data Analysis 2 Journal of Mathematical Imaging and Vision 2 International Journal of Theoretical and Applied Finance 2 Journal of Industrial and Management Optimization 2 Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya Matematika 2 EURO Journal on Computational Optimization 2 Universitext 1 Computer Physics Communications 1 Discrete Applied Mathematics 1 Journal of the Mechanics and Physics of Solids 1 Mathematics of Computation 1 Bulletin of Mathematical Biology 1 The Annals of Statistics 1 Applied Mathematics and Computation 1 Applied Mathematics and Optimization 1 BIT 1 Mathematics of Operations Research 1 Numerical Functional Analysis and Optimization 1 Numerische Mathematik 1 SIAM Journal on Numerical Analysis 1 Systems & Control Letters 1 Chinese Annals of Mathematics. Series B 1 Acta Mathematicae Applicatae Sinica. English Series 1 SIAM Journal on Matrix Analysis and Applications 1 Journal of Scientific Computing 1 Journal of Parallel and Distributed Computing 1 Machine Learning 1 Neural Computation 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Numerical Algorithms 1 Computational Mathematics and Mathematical Physics 1 Automation and Remote Control 1 Linear Algebra and its Applications 1 SIAM Review 1 Statistical Papers 1 Computational and Applied Mathematics 1 Annals of Mathematics and Artificial Intelligence 1 Mathematical Problems in Engineering 1 Mathematical Methods of Operations Research 1 Interdisciplinary Information Sciences (IIS) 1 Computational Geosciences 1 Nonlinear Analysis. Real World Applications 1 Discrete and Continuous Dynamical Systems. Series B 1 Structural and Multidisciplinary Optimization 1 4OR 1 International Journal of Computational Methods 1 Mediterranean Journal of Mathematics 1 Computational Management Science 1 International Journal of Numerical Analysis and Modeling 1 Discrete Optimization 1 Advances in Data Analysis and Classification. ADAC 1 Communications in Computational Physics 1 Networks and Heterogeneous Media 1 SIAM Journal on Imaging Sciences 1 Discrete and Continuous Dynamical Systems. Series S 1 Mathematical Geosciences 1 The Journal of Computational Finance 1 Journal of Control Science and Engineering 1 Mathematical Programming Computation 1 Pacific Journal of Mathematics for Industry 1 AIMS Mathematics 1 SN Operations Research Forum
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### Cited in 28 Fields

 130 Operations research, mathematical programming (90-XX) 80 Numerical analysis (65-XX) 47 Calculus of variations and optimal control; optimization (49-XX) 14 Partial differential equations (35-XX) 13 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 13 Systems theory; control (93-XX) 11 Mechanics of deformable solids (74-XX) 9 Statistics (62-XX) 8 Computer science (68-XX) 8 Biology and other natural sciences (92-XX) 5 Fluid mechanics (76-XX) 5 Geophysics (86-XX) 5 Information and communication theory, circuits (94-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Integral equations (45-XX) 2 Functional analysis (46-XX) 2 Probability theory and stochastic processes (60-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Ordinary differential equations (34-XX) 1 Convex and discrete geometry (52-XX) 1 Quantum theory (81-XX) 1 Astronomy and astrophysics (85-XX)