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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Vydáno v:Mathematical programming Ročník 100; číslo 1; s. 27
Hlavní autoři: Byrd, Richard H., Gould, Nicholas I.M., Nocedal, Jorge, Waltz, Richard A.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Heidelberg Springer Nature B.V 01.05.2004
Témata:
Algorithms
Computer engineering
Grants
Linear programming
Methods
Optimization
Quadratic programming
ISSN:0025-5610, 1436-4646
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-003-0485-4