THE SLACKED UNCONSTRAINED MINIMIZATION TECHNIQUE FOR CONVEX PROGRAMMING.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1966
- Accession Number
- AD0643817
Entities
People
- Anthony V. Fiacco
- Garth P. Mccormick