Journal of the Australian Mathematical Society (Series A)

Table of Contents - 1981 - Volume 30, Issue 03  

Research Article

Facial reduction for a cone-convex programming problem

Jon M. Borweina1 and Henry Wolkowicza2

a1 Department of Mathematics, Dalhousie University, Halifax, Canada

a2 Department of Mathematics, University of Alberta, Edmonton, Canada

Abstract

In this paper we study the abstract convex program

S1446788700017250_eqnU1

where S is an arbitrary convex cone in a finite dimensional space, Ω is a convex set and p and g are respectively convex and S (on Ω). We use the concept of a minimal cone for (P) to correct and strengthen a previous characterization of optimality for (P), see Theorem 3.2. The results presented here are used in a sequel to provide a Lagrange multiplier theorem for (P) which holds without any constraint qualification.

(Received March 21 1980)

(Revised July 28 1980)

1980 Mathematics subject classification (Amer. Math. Soc.)

  • 90 C 25

Keywords

  • Convexity;
  • abstract programming;
  • facial reduction;
  • exposed face