Concerning classes of iterative-optimization solution techniques and their applications

Abstract

This dissertation is concerned with the following optimization problem: P[subscript o]: min H[p(x), f(x)] where x = (x1, x2, ...,xn), X is a compact-convex subset of R[superscript n] with f and p functions from R[superscript n] into R[superscript m]. Further, H is a convex functional involving p and f. In many industrial problems, the function p has no explicit mathematical representation. In such instances, one of two solutions procedures to P[subscript o] can be applied: (i) Derive a mathematical expression which approximates p and then solve the related explicit mathematical problem by using an existing solution technique. The solution obtained in this manner is, of course, not the true solution of P[subscript o]. The accuracy of the solution of this related problem to that of the true solution to P[subscript o] is dependent upon the accuracy of the mathematical representation of p as well as the sensitivity of H with respect to p.