A robust implementation of a sequential quadratic programming algorithm with successive error restoration

We consider sequential quadratic programming methods for solving constrained nonlinear programming problems. It is generally believed that these methods are sensitive to the accuracy by which partial derivatives are provided. One reason is that differences of gradients of the Lagrangian function are...

Full description

Saved in:
Bibliographic Details
Published in:Optimization letters Vol. 5; no. 2; pp. 283 - 296
Main Author: Schittkowski, K.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.05.2011
Subjects:
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
Line search
SQP
Sequential quadratic programming
Nonlinear programming
Restart
Noisy functions
Numerical algorithm
ISSN:1862-4472, 1862-4480
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider sequential quadratic programming methods for solving constrained nonlinear programming problems. It is generally believed that these methods are sensitive to the accuracy by which partial derivatives are provided. One reason is that differences of gradients of the Lagrangian function are used for updating a quasi-Newton matrix, e.g., by the BFGS formula. The purpose of this paper is to show by numerical experimentation that the method can be stabilized substantially. The algorithm applies non-monotone line search and internal and external restarts in case of errors due to inaccurate derivatives while computing the search direction. Even in case of large random errors leading to partial derivatives with at most one correct digit, termination subject to an accuracy of 10 −7 can be achieved in 90% of 306 problems of a standard test suite. On the other hand, the original version with monotone line search and without restarts solves only 30% of these problems under the same test environment. In addition, we show how initial and periodic scaled restarts improve the efficiency in situations with slow convergence.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-010-0207-9