On "two important theorems" in canonical duality theory

TL;DR

This paper critically examines two theorems in canonical duality theory, providing counterexamples that demonstrate their falsehood, thereby challenging recent claims in the literature.

Contribution

It identifies errors in two key theorems of canonical duality theory through counterexamples, clarifying the theory's limitations.

Findings

Counterexamples invalidate the two theorems

The theorems are false in general

Challenges recent claims in the literature

Abstract

In this short note we show, providing counterexamples, that the "two important theorems" in the recent paper [Y, Yuan, Global optimization solutions to a class of non-convex quadratic minimization problems with quadratic constraints, in Canonical Duality Theory, D.Y. Gao et al.\ (eds), (AMMA, volume 37), Springer, 2017] are false.