An algorithm for nonlinear optimization using linear programming and equality constrained subproblems

This paper describes an active-set algorithm for large-scale nonlinear programming based on the successive linear programming method proposed by Fletcher and Sainz de la Maza [10]. The step computation is performed in two stages. In the first stage a linear program is solved to estimate the active s...

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Bibliographic Details
Published in:Mathematical programming Vol. 100; no. 1; p. 27
Main Authors: Byrd, Richard H., Gould, Nicholas I.M., Nocedal, Jorge, Waltz, Richard A.
Format: Journal Article
Language:English
Published: Heidelberg Springer Nature B.V 01.05.2004
Subjects:
Algorithms
Computer engineering
Grants
Linear programming
Methods
Optimization
Quadratic programming
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary:This paper describes an active-set algorithm for large-scale nonlinear programming based on the successive linear programming method proposed by Fletcher and Sainz de la Maza [10]. The step computation is performed in two stages. In the first stage a linear program is solved to estimate the active set at the solution. The linear program is obtained by making a linear approximation to the [cursive l]<1< penalty function inside a trust region. In the second stage, an equality constrained quadratic program (EQP) is solved involving only those constraints that are active at the solution of the linear program. The EQP incorporates a trust-region constraint and is solved (inexactly) by means of a projected conjugate gradient method. Numerical experiments are presented illustrating the performance of the algorithm on the CUTEr [1, 15] test set.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-003-0485-4