A Generalized Reduced Gradient Approach for Solving a Class of Two-Stage Stochastic Nonlinear Programs

Abstract

Two-stage stochastic programming problems arise in many practical sit-uations, such as production and manpower planning, portfolio selections and so on. In general, the deterministic equivalences of these problems can be very large, and may not be solvable directly by general-purpose optimization approaches. Reduced gradient method (RGM) is a well known technique for nonlinear programming problems. After using scenario analysis technique, a direct search approach based on RGM for solving a class of two-stage stochastic nonlinear programs is proposed, which generates the search direction by solving parallelly a set of quadratic programming subproblems with size much less than the original problem at each iteration. By selecting the step-size to reduce an exact penalty function sufficiently, the algorithm terminates at an approximate optimal solution to the problem with any desirable accuracy.