Ekeland's variational principle for weighted set relation with set perturbation and application to game theory
Yousuke Araya, Pradeep Kumar Sharma, Wei–Shih Du · Optimization · 2025
In this paper, we introduce cancellation laws for weighted set relations, which are a mixture of lower and upper set relations. Applying nonlinear scalarizing techniques for sets, we propose a new type of minimal element theorem and generalized Ekeland's variational principles for weighted set relation with set perturbation. An application of generalized Ekeland's variational principles is given to vector-valued game theory under uncertainty.