Global solutions to general polynomial benchmark optimization problems

TL;DR

This paper introduces a generalized canonical duality approach to efficiently find global solutions for high-order polynomial benchmark optimization problems, transforming complex nonconvex problems into solvable dual forms without duality gaps.

Contribution

The paper develops a novel generalized canonical duality method that guarantees global solutions for a broad class of polynomial optimization problems, including classical benchmarks.

Findings

Successfully solves Goldstein-Price and Three Hump Camel Back problems.

Transforms nonconvex problems into convex dual problems without duality gap.

Provides a practical approach for global optimization of polynomial problems.

Abstract

The goal of this paper is to solve a class of high-order polynomial benchmark optimization problems, including the Goldstein-Price problem and the Three Hump Camel Back problem. By using a generalized canonical duality theory, we are able to transform the nonconvex primal problems to concave dual problems over convex domain(without duality gap), which can be solved easily to obtain global solutions.