On global solvability of a class of possibly nonconvex QCQP problems in Hilbert spaces

We provide conditions ensuring that the KKT-type conditions characterizes the global optimality for quadratically constrained (possibly nonconvex) quadratic programming QCQP problems in Hilbert spaces. The key property is the convexity of a image-type set related to the functions appearing in the formulation of the problem. The proof of the main result relies on a generalized version of the (Jakubovich) S-Lemma in Hilbert spaces. As an application, we consider the class of QCQP problems with a special form of the quadratic terms of the constraints.Comment: arXiv admin note: text overlap with arXiv:2206.0061

Strong pseudomonotonicity, sharp efficiency and stability for parametric vector equilibria

We investigate Hőlder type estimates of solutions to parametric vector equilibrium problems. Our results rely on the notion of strong pseudomonotonicity of the bifunctions defining problems. When applied to vector optimization problems, the strong pseudomonotonicity introduced in the present paper implies the uniform (with the same constant) sharpness of solutions

Bishop-Phelps cones and convexity: applications to stability of vector optimization problems

In this report we study the stability of cone support points Min(A|K) of a given set A in a topological vector space Y, equipped with a closed convex cone K \subset Y. We prove sufficient conditions for the lower continuity of Min(A|K) when A is subjected to perturbations (Theorem 2.2, Theorem 2.3). The crucial assumption is that the set Min(AjK) is dense in the set of strict cone support points (Definition 2.1). In normed vector spaces Y the set of strict support points contains the set of super efficient points in the sense of Borwein and Zhuang. By making use of the density result for super efficient points Theorem 4.2 gives sufficient conditions for the lower continuity of cone support points for cones with weakly compact bases and the original set A being closed and convex. When K is a Bishop-Phelps cone in a Banach space Y we give a simple characterisation of strict support points (Theorem 3.2) which allows us to give a variant of the result of Attouch and Riahi (Theorem 3.4) without a..