A Duality Theorem for Nonlinear Programming

Abstract

One reasonable formulation of stochastic linear programming problem leads to a deterministic nonlinear programming problem where the non-linearity occurs in the objective function as the sum of square roots of positive semi-definite quadratic forms. It may, however, be difficult to solve this problem directly because of the nondifferentiability of the terms in the objective function. The present paper establishes a dual to the nonlinear programming problem of which a solution may be easily obtained. A solution of the dual then helps to obtain a solution of the original problem.