Differential Inclusions, Control and Optimization 20 (2000) 171-194
doi: 10.7151/dmdico.1011

[BIBTex] [PDF] [PS]

LARGE-SCALE NONLINEAR PROGRAMMING ALGORITHM USING PROJECTION METHODS

Paweł Białoń

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

e-mail: P.Bialon@itl.waw.pl

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: nonlinear optimization, large scale optimization, projection methods, zigzagging.

1991 Mathematics Subject Classification: 65M99, 49M45, 49M27, 65-06, 90C06, 90C99.

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Received 17 November 1999
Revised 15 October 2000