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<p>This paper investigates sufficient conditions for the existence of solutions to the convex quadratic programming problem with an arbitrary nonempty, closed, and convex constraint set in Hilbert spaces. Additionally, it focuses on the qualitative stability of the solution set and the optimal value function under perturbations of the objective function. Our results contribute to the study of quadratic optimization problems with arbitrary closed convex constraint sets in infinite-dimensional Hilbert spaces.</p>

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Sufficient conditions for the existence and stability of solutions to convex quadratic programs in Hilbert spaces

  • 期刊论文

  • 发表日期：

    2026年6月1日

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  • Vu Van Dong

摘要

This paper investigates sufficient conditions for the existence of solutions to the convex quadratic programming problem with an arbitrary nonempty, closed, and convex constraint set in Hilbert spaces. Additionally, it focuses on the qualitative stability of the solution set and the optimal value function under perturbations of the objective function. Our results contribute to the study of quadratic optimization problems with arbitrary closed convex constraint sets in infinite-dimensional Hilbert spaces.