A Simple But Effective Canonical Dual Theory Unified Algorithm for Global Optimization

TL;DR

This paper introduces a simple yet effective canonical duality theory-based algorithm for global optimization, demonstrating its convergence and efficiency in solving high-dimensional nonconvex and nonsmooth problems with zero dual gap.

Contribution

It proposes a novel unified algorithm based on canonical duality theory that is simple, convergent, and effective for high-dimensional nonconvex/nonsmooth optimization problems.

Findings

Proves convergence of the CDT-based algorithm.

Shows the algorithm finds global optima with zero dual gap.

Demonstrates effectiveness on both low- and high-dimensional problems.

Abstract

Numerical global optimization methods are often very time consuming and could not be applied for high-dimensional nonconvex/nonsmooth optimization problems. Due to the nonconvexity/nonsmoothness, directly solving the primal problems sometimes is very difficult. This paper presents a very simple but very effective canonical duality theory (CDT) unified global optimization algorithm. This algorithm has convergence is proved in this paper. More important, for this CDT-unified algorithm, numerous numerical computational results show that it is very powerful not only for solving low-dimensional but also for solving high-dimensional nonconvex/nonsmooth optimization problems, and the global optimal solutions can be easily and elegantly got with zero dual gap.