Extended reverse-convex programming: an approximate enumeration approach to global optimization

TL;DR

This paper introduces an approximate enumeration method for solving factorable nonlinear programming problems to global optimality by transforming them into reverse-convex programming problems and solving via enumeration, with theoretical guarantees.

Contribution

It presents a novel approach that approximates NLP problems with RCP problems and guarantees global optimality through the concept of RCP regularity.

Findings

Enumeration guarantees global optimality for regular RCP problems.

The extended RCP algorithm performs well on test problems.

Theoretical framework ensures solution accuracy.

Abstract

A new approach to solving a large class of factorable nonlinear programming (NLP) problems to global optimality is presented in this paper. Unlike the traditional strategy of partitioning the decision-variable space employed in many branch-and-bound methods, the proposed approach approximates the NLP problem by a reverse-convex programming (RCP) problem to a controlled precision, with the latter then solved by an enumerative search. To establish the theoretical guarantees of the method, the notion of "RCP regularity" is introduced and it is proven that enumeration is guaranteed to yield a global optimum when the RCP problem is regular. An extended RCP algorithmic framework is then presented and its performance is examined for a small set of test problems.