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

We provide solution existence results for the convex quadratic programming problems in Hilbert spaces, which the constraint set is defined by finitely many convex quadratic inequalities. In order to obtain our results, we shall use either the properties of the Legendre form or the properties of the...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 20; no. 6; pp. 1417 - 1436
Main Authors Van Dong, Vu, Tam, Nguyen Nang
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.12.2016
Subjects
Coercivity
Existence theorems
Hilbert spaces
Objective functions
Quadratic programming
Topological compactness
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Summary:We provide solution existence results for the convex quadratic programming problems in Hilbert spaces, which the constraint set is defined by finitely many convex quadratic inequalities. In order to obtain our results, we shall use either the properties of the Legendre form or the properties of the finite-rank operator. The existence results are established without requesting neither coercivity of the objective function nor compactness of the constraint set.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.20.2016.6936