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A note on Legendre-Fenchel conjugate of the product of two positive-definite quadratic forms

Xia Yong (dearyxia***at***gmail.com)

Abstract: The Legendre-Fenchel conjugate of the product of two positive-definite quadratic forms was posted as an open question in the field of nonlinear analysis and optimization by Hiriart-Urruty [`Question 11' in {\it SIAM Review} 49, 255-273, (2007)]. Under a convex assumption on the function, it was answered by Zhao [SIAM J. Matrix Analysis $\&$ Applications, 31(4), 1792-1811 (2010)]. In this note, we answer the open question without making the convexity assumption.

Keywords: Legendre-Fenchel conjugate, quadratic form

Category 1: Global Optimization (Theory )

Category 2: Nonlinear Optimization (Unconstrained Optimization )

Citation: Yong Xia, A note on Legendre-Fenchel conjugate of the product of two positive-definite quadratic forms, Journal of Operations Research Society of China, to appear, 2013

Download: [PDF]

Entry Submitted: 04/26/2013
Entry Accepted: 05/01/2013
Entry Last Modified: 07/08/2013

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