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

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

We propose conditions for the existence of solutions for nonconvex quadratic programming problems whose constraint set is defined by finitely many convex linear-quadratic inequalities in Hilbert spaces. In order to obtain our results, we use either properties of the Legendre form or properties of co...

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Veröffentlicht in:Acta mathematica vietnamica 2018-03, Vol.43 (1), p.155-174
Hauptverfasser: Dong, Vu Van, Tam, Nguyen Nang
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Convexity
Hilbert space
Mathematics
Mathematics and Statistics
Quadratic programming
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Tam, Nguyen Nang
description We propose conditions for the existence of solutions for nonconvex quadratic programming problems whose constraint set is defined by finitely many convex linear-quadratic inequalities in Hilbert spaces. In order to obtain our results, we use either properties of the Legendre form or properties of compact operators with closed range. The results are established without requesting the convexity of the objective function or the compactness of the constraint set. As a special case, we obtain some on the existence of solutions results for the quadratic programming problems under linear constraints in Hilbert spaces.
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subjects Convexity
Hilbert space
Mathematics
Mathematics and Statistics
Quadratic programming
title On the Solution Existence of Nonconvex Quadratic Programming Problems in Hilbert Spaces
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