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

Orestes Bueno (), John Cotrina () and Yboon García
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Orestes Bueno: Universidad del Pacífico
John Cotrina: Universidad del Pacífico

Journal of Optimization Theory and Applications, 2023, vol. 198, issue 3, No 14, 1246-1263

Abstract: Abstract 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.

Keywords: Maximal elements; Stampacchia variational inequality; Minty variational inequality; Steepest descent method; 91B16; 49J40; 49J53 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02251-y

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