On the Solution Existence of Convex Quadratic Programming Problems in Hilbert Spaces
Vu Van Dong, Nguyen Nang Tam · Taiwanese Journal of Mathematics · 2016
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.