A Note on Legendre-Fenchel Conjugate of the Product of Two Positive-Definite Quadratic Forms

Yong Xia

doi:10.1007/s40305-013-0018-7

A Note on Legendre-Fenchel Conjugate of the Product of Two Positive-Definite Quadratic Forms

Yong Xia^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 SIAM Review 49, 255-273, 2007]. Under a convexity assumption on the function, it was answered by Zhao [SIAM J. Matrix Analysis & Applications31(4), 1792-1811, 2010]. In this note, we answer the open question without making the convexity assumption.

Original language	English
Pages (from-to)	333-338
Number of pages	6
Journal	Journal of the Operations Research Society of China
Volume	1
Issue number	3
DOIs	https://doi.org/10.1007/s40305-013-0018-7
State	Published - Sep 2013

Keywords

Legendre-Fenchel conjugate
Quadratic form

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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 SIAM Review 49, 255-273, 2007]. Under a convexity assumption on the function, it was answered by Zhao [SIAM J. Matrix Analysis \& Applications31(4), 1792-1811, 2010]. In this note, we answer the open question without making the convexity assumption.",

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KW - Legendre-Fenchel conjugate

KW - Quadratic form

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ER -

A Note on Legendre-Fenchel Conjugate of the Product of Two Positive-Definite Quadratic Forms

Abstract

Keywords

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