Abstract

It is known that stability is a fundamental and important topic in optimization theory. The main objective of this field is to study of behavior of solutions to parametric problems when the data of the problems undergoes small changes. Therefore, stability for optimization-related problems holds both theoretical and practical significance, which has been used as a useful tool in post-optimal analysis. As usual, the stability can be understood in two ways: the first involves the upper and lower semicontinuity and the continuity of solution maps to parametric problems, referred to as qualitative stability; the second encompasses the Hölder/Lipschitz continuity of solution maps of the problems, termed quantitative stability. For parametric problems with the parameters perturbed in spaces of parameters, several researchers have established various types of stability conditions, drawing on the continuity properties of objective maps and constrained maps, along with their convexity and monotonicity properties. In this paper, we are concerned with parametric vector equilibrium problems in noremed spaces and aim at to improve some recent results. To achieve this, we first introduce a relaxed concept of cone-quasiconcavity, specifically the cone-lower level quasiconcavity. Also, necsessary and sufficient conditions are investigated. We provide an example to illustrate that this new condition is strictly weaker than the cone-quasiconcavity. After that, we employ this new condition together with Hölder properties of the constrained map and the objective map to establish sufficient conditions for the stability in the sense of Hölder continuity of solution maps for the reference problems via the linear scalarization method. A special case of the reference problems is also discussed. Our results in this paper represent improvements over the existing ones in the literature.