- A note on Legendre-Fenchel conjugate of the product of two positive-definite quadratic forms Xia Yong (dearyxiagmail.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: 04/26/2013Entry Accepted: 05/01/2013Entry Last Modified: 07/08/2013Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.