Existence and uniqueness of maximal elements for preference relations: Variational approach

Orestes Bueno; John Cotrina; Yboon García

doi:10.1007/s10957-023-02251-y

Existence and uniqueness of maximal elements for preference relations: Variational approach

Orestes Bueno, John Cotrina, Yboon García

Producción científica: Contribución a una revista › Artículo de revista › revisión exhaustiva

Resumen

En este trabajo, reformulamos el problema de la existencia de elementos maximales para relaciones de preferencia como un problema de desigualdad variacional en el sentido de Stampacchia. Del mismo modo, establecemos la unicidad de elementos maximales utilizando un problema de desigualdad variacional en el sentido de Minty. En ambos enfoques, utilizamos el operador de cono normal para encontrar resultados de existencia y unicidad, bajo suposiciones moderadas. Además, proporcionamos un algoritmo para encontrar tales elementos maximales, inspirado en el método de descenso más pronunciado para la minimización. Bajo ciertas condiciones, demostramos que la secuencia generada por este algoritmo converge a un elemento maximal.

Idioma original	Inglés
Páginas (desde-hasta)	1246-1263
Número de páginas	18
Publicación	Journal of Optimization Theory and Applications
Volumen	198
N.º	3
Fecha en línea anticipada	27 jul. 2023
DOI	https://doi.org/10.1007/s10957-023-02251-y
Estado	Publicada - set. 2023

Nota bibliográfica

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Funding Information:
We would like to thank the anonymous referee for their valuable remarks and suggestions, which have undoubtedly enhanced the quality of this work. Additionally, we extend our appreciation for pointing us toward Example 3.4.

Palabras clave

Elementos máximos
Desigualdad variacional de Minty
Desigualdad variacional de Stampacchia
Método de descenso más pronunciado

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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.",

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AU - Bueno, Orestes

AU - Cotrina, John

AU - García, Yboon

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N2 - 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.

AB - 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.

KW - Maximal elements

KW - Minty variational inequality

KW - Stampacchia variational inequality

KW - Steepest descent method

KW - Elementos máximos

KW - Desigualdad variacional de Minty

KW - Desigualdad variacional de Stampacchia

KW - Método de descenso más pronunciado

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DO - 10.1007/s10957-023-02251-y

M3 - Article in a journal

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SN - 0022-3239

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JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

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Existence and uniqueness of maximal elements for preference relations: Variational approach

Resumen

Nota bibliográfica

Palabras clave

ODS de las Naciones Unidas

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