On the Solution Existence of Nonconvex Quadratic Programming Problems in Hilbert Spaces

2016/04/17 by Vu Van Dong, Van Dong, Vu, Nguyen Nang Tam +1
Computer Science · Mathematics · #90C20 #90C26 #90C30 #Advanced Optimization Algorithms Research #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #math.OC #msc:90C20 #msc:90C26 #msc:90C30

paper · pdf · doi:10.48550/arxiv.1604.04841

openalex publication_date 2016/04/17 · arxiv created 2016/04/29 · arxiv updated 2016/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the quadratic programming problems under finitely many convex quadratic constraints in Hilbert spaces. By using the Legendre property of quadratic forms or the compactness of operators in the presentations of quadratic forms, we establish some sufficient conditions for the solution existence of the considered problems. As special cases, we obtain some existence solution results for the quadratic programming problems under linear constraints in Hilbert spaces.

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