Some remarks on quadratic programming with 0-1 variables

Abstract

The aim of this paper is to show that every bivalent (0,1)quadratic programming problem is equivalent to one having apositive (negative) semi-definite matrix in the objectivefunction, to establish conditions for different classes oflocal optimality, and to show that any problem of bivalent(0,1) programming is equivalent (a) to the problem ofminimizing a real valued function, partly in (0,1) andpartly in non-negative variables, (b) to the problem offinding the minimax of a real valued function in bivalent(0,1) variables.