On the Realization of the Wolfe Conditions in Reduced Quasi-Newton Methods for Equality Constrained Optimization

This paper describes a reduced quasi-Newton method for solving equality constrained optimization problems. A major difficulty encountered by this type of algorithm is the design of a consistent technique for maintaining the positive definiteness of the matrices approximating the reduced Hessian of t...

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Bibliographic Details
Published in:SIAM journal on optimization Vol. 7; no. 3; pp. 780 - 813
Main Author: Gilbert, Jean Charles
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.08.1997
Subjects:
Algorithms
Approximation
Computer Science
Optimization
Other
Quadratic programming
ISSN:1052-6234, 1095-7189
Online Access:Get full text
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Summary:This paper describes a reduced quasi-Newton method for solving equality constrained optimization problems. A major difficulty encountered by this type of algorithm is the design of a consistent technique for maintaining the positive definiteness of the matrices approximating the reduced Hessian of the Lagrangian. A new approach is proposed in this paper. The idea is to search for the next iterate along a piecewise linear path. The path is designed so that some generalized Wolfe conditions can be satisfied. These conditions allow the algorithm to sustain the positive definiteness of the matrices from iteration to iteration by a mechanism that has turned out to be efficient in unconstrained optimization.
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ISSN:1052-6234
1095-7189
DOI:10.1137/S1052623493259604