article

SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization

Authors:

Philip E. Gill,

Walter Murray,

Michael A. SaundersAuthors Info & Claims

SIAM Journal on Optimization, Volume 12, Issue 4

Pages 979 - 1006

https://doi.org/10.1137/S1052623499350013

Published: 01 April 2002 Publication History

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Abstract

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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cover image SIAM Journal on Optimization

SIAM Journal on Optimization Volume 12, Issue 4

2002

286 pages

ISSN:1052-6234

Issue’s Table of Contents

Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 April 2002

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Burachik RKaya CMoursi W(2024)Infeasible and Critically Feasible Optimal ControlJournal of Optimization Theory and Applications10.1007/s10957-024-02419-0203:2(1219-1245)Online publication date: 1-Nov-2024
https://dl.acm.org/doi/10.1007/s10957-024-02419-0
Gill PZhang M(2024)A projected-search interior-point method for nonlinearly constrained optimizationComputational Optimization and Applications10.1007/s10589-023-00549-188:1(37-70)Online publication date: 1-May-2024
https://dl.acm.org/doi/10.1007/s10589-023-00549-1
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