On the Solution Existence of Nonconvex Quadratic Programming Problems in Hilbert Spaces
Vu Van Dong
,
Nguyen Nang Tam
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.
Viện Toán học, Viện Hàn lâm Khoa học và Công nghệ Việt Nam
Địa chỉ: Số 18 đường Hoàng Quốc Việt, quận Cầu Giấy, Hà Nội
Điện thoại: 024 37563474 - Fax: 024 37564303
Email: vientoan@math.ac.vn
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