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ArticleOriginal scientific text

Title

Large-scale nonlinear programming algorithm using projection methods

Authors 1

Affiliations

  1. National Institute of Telecommunications, Decision Support System Laboratory, ul. Szachowa 1, 04-894 Warszawa, Poland

Abstract

A method for solving large convex optimization problems is presented. Such problems usually contain a big linear part and only a small or medium nonlinear part. The parts are tackled using two specialized (and thus efficient) external solvers: purely nonlinear and large-scale linear with a quadratic goal function. The decomposition uses an alteration of projection methods. The construction of the method is based on the zigzagging phenomenon and yields a non-asymptotic convergence, not dependent on a large dimension of the problem. The method preserves its convergence properties under limitations in complicating sets by geometric cuts. Various aspects and variants of the method are analyzed theoretically and experimentally.

Keywords

ENG
nonlinear optimization, large scale optimization, projection methods, zigzagging

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Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2000/20/2
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Pages:
171-194
Main language of publication
English
Received
1999-11-17
Accepted
2000-10-15
Published
2000

DOI: 10.7151/dmgt.1011

Exact and natural sciences