1,721,047 research outputs found
Scalarization and decomposition of vector variational inequalities governed by bifunctions
No full textIn this article we study the structure of solution sets within a special class of generalized Stampacchia-type vector variational inequalities, defined by means of a bifunction which takes values in a partially ordered Euclidean space. It is shown that, similar to multicriteria optimization problems, under appropriate convexity assumptions, the (weak) solutions of these vector variational inequalities can be recovered by solving a family of weighted scalar variational inequalities. Consequently, it is deduced that the set of weak solutions can be decomposed into the union of the sets of strong solutions of all variational inequalities obtained from the original one by selecting certain components of the bifunction which governs it
Distributionally robust multiobjective optimization with application to risk measure theory
No full textWe introduce the concept of a distributionally robust multiobjective optimization problem, which offers a comprehensive framework for addressing issues related to the statistical estimation of unknown probabilities. By employing scalarization methods, we establish optimality conditions, followed by the exploration of applications in financial portfolio management and risk assessment
- …
