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

Research paper by Vu Van Dong, Nguyen Nang Tam

Indexed on: 29 Apr '16Published on: 29 Apr '16Published in: Mathematics - Optimization and Control



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.