A necessary and sufficient condition for minimizing a convex Frechet differentiable function on a certain hyperplane

Abstract

A convex Frechet differentiable function is minimized subject to a certain hyperplane at a point if the function is minimized in all directions which are defined by a finite set of vectors. The proposed approach is different from the Lagrange multiplier approach. At the end of this paper, a linear program is formulated to solve the case when the above given convex function is quadratic. (C) 2001 Academic Press.