On Minimizing a Convex Function Subject to Linear Inequalities

Abstract

Summary The minimization of a convex function of variables subject to linear inequalities is discussed briefly in general terms. Dantzig’s Simplex Method is extended to yield finite algorithms for minimizing either a convex quadratic function or the sum of the t largest of a set of linear functions, and the solution of a generalization of the latter problem is indicated. In the last two sections a form of linear programming with random variables as coefficients is described, and shown to involve the minimization of a convex function.