logo_acta

Acta Mathematica Vietnamica

A LINEAR PROGRAMMING APPROACH TO SOLVING A JOINTLY CONSTRAINED BILINEAR PROGRAMMING PROBLEM WITH SPECIAL STRUCTURE

icon-email TRAN VU THIEU

Abstract

In this paper we shall deal with the following nonconvex optimization problem: (P) Minimize cTz, subject to zD and zi=xiyi for all i=1,,pn,xX,yS,  where D,S are polyhedrons in Rn, Rp respectively, X={xRp|0<axA}; a,A are p-vectors; c is an n-vector. It is shown that (P) can be reduced to a linear program whose constraints can explicitly be given in some special cases.