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Simplex-Like Trajectories on Quasi-Polyhedral Sets

Australian Graduate School of Management, University of New South Wales, Sydney 2052, Australia
Department of Statistics and Operations Research, Faculty of Sciences, University of Alicante, 03071 Alicante, Spain
Department of Statistics and Operations Research, Faculty of Sciences, University of Alicante, 03071 Alicante, Spain

This paper presents a unified treatment of two new simplex-like methods for linear semi-infinite programming problems with quasi-polyhedral feasible sets. The simplex method combines a purification phase I (which provides an extreme point from a given feasible solution) with the iterative application of a pivot operation, yielding a trajectory which consists of a (possibly infinite) sequence of linked edges (phase II). The reduced gradient method also consists of two phases and it can be applied even when the feasible set has no extreme point.

Key Words: Semi-infinite programming; simplex-like algorithms; locally polyhedral systems; quasi-polyhedral sets
History: Received: May 6, 1997; revision received: December 7, 1998;revision received: February 24, 2000;revision received: June 28, 2000;