Existence and Uniqueness of Maximal Elements for Preference Relations: Variational Approach

Bueno O.; Cotrina J.; García Y. · Journal of Optimization Theory and Applications (2023) · DOI: 10.1007/s10957-023-02251-y

Resumen

In this work, we reformulate the problem of existence of maximal elements for preference relations as a variational inequality problem in the sense of Stampacchia. Similarly, we establish the uniqueness of maximal elements using a variational inequality problem in the sense of Minty. In both of these approaches, we use the normal cone operator to find existence and uniqueness results, under mild assumptions. In addition, we provide an algorithm for finding such maximal elements, which is inspired by the steepest descent method for minimization. Under certain conditions, we prove that the sequence generated by this algorithm converges to a maximal element.

Instituciones: Universidad del Pacífico