On quadratic optimization problems and canonical duality theory

TL;DR

This paper rigorously analyzes quadratic optimization problems using Canonical Duality Theory (CDT), clarifying previous ambiguities and comparing new results with earlier work by DY Gao and colleagues.

Contribution

It provides a rigorous treatment of quadratic optimization problems with CDT, addressing previous unclear definitions and flawed proofs, and offers a comparative analysis with prior results.

Findings

Clarified the definitions and proofs of CDT in quadratic optimization

Identified and corrected inaccuracies in previous CDT applications

Provided new, rigorous solutions consistent with or improving upon prior results

Abstract

DY Gao solely or together with some of his collaborators applied his Canonical duality theory (CDT) for solving some quadratic optimization problems with quadratic constraints. Unfortunately, in almost all papers we read on CDT there are unclear definitions, non convincing arguments in the proofs, and even false results. The aim of this paper is to treat rigorously quadratic optimization problems by the method suggested by CDT and to compare what we get with the results obtained by DY Gao and his collaborators on this topic in several papers.