Accession Number : AD0643817

Title :   THE SLACKED UNCONSTRAINED MINIMIZATION TECHNIQUE FOR CONVEX PROGRAMMING.

Descriptive Note : Technical paper,

Corporate Author : RESEARCH ANALYSIS CORP MCLEAN VA

Personal Author(s) : Fiacco,Anthony V. ; McCormick,Garth P.

Report Date : AUG 1966

Pagination or Media Count : 21

Abstract : An algorithm for solving the problem: minimize f (x) (a convex function) subject to g sub i (x) or = 0, i = 1, . . . , m (g sub i a concave function) is presented. Specifically the function P(x,t,r sub k) is identical with f(x) + 1/r sub k sigma (g sub i (x) - t sub i)squared is minimized over all x, nonnegative t, for a strictly decreasing null sequence (r sub k). It is proved that for every r sub k > 0, there exists a finite point (x (r sub k), t(r sub k)) which minimizes P and solves the convex programming problems as r sub k approaches 0. This algorithm is similar to the Sequential Unconstrained Minimization Technique (SUMT) found in a work by Fiacco and McCormick, in that it solves Wolfe's dual programming problem. It differs from SUMT in that (a) it approaches the optimum from the region of infeasibility (i,e., it is a relaxation technique), (b) it does not require a nonempty interior to the nonlinearly constrained region, (c) no separate feasibility phase is required before optimization takes place, and (d) the computational effort to solve the problem drastically reduced. (Author)

Descriptors :   (*NONLINEAR PROGRAMMING, ALGORITHMS), (*OPTIMIZATION, NONLINEAR PROGRAMMING), SEQUENCES(MATHEMATICS), FUNCTIONS(MATHEMATICS), EQUATIONS, THEOREMS

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE