Artículo
Solutions of Optimization Problems on Hadamard Manifolds with Lipschitz Functions
Autor/es | Ruiz Garzón, Gabriel
Osuna Gómez, Rafaela Rufián Lizana, Antonio |
Departamento | Universidad de Sevilla. Departamento de Estadística e Investigación Operativa |
Fecha de publicación | 2020-05 |
Fecha de depósito | 2023-04-13 |
Publicado en |
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Resumen | The aims of this paper are twofold. First, it is shown, for the first time, which types of
nonsmooth functions are characterized by all vector critical points as being efficient or weakly efficient
solutions of vector ... The aims of this paper are twofold. First, it is shown, for the first time, which types of nonsmooth functions are characterized by all vector critical points as being efficient or weakly efficient solutions of vector optimization problems in constrained and unconstrained scenarios on Hadamard manifolds. This implies the need to extend different concepts, such as the Karush–Kuhn–Tucker vector critical points and generalized invexity functions, to Hadamard manifolds. The relationships between these quantities are clarified through a great number of explanatory examples. Second, we present an economic application proving that Nash’s critical and equilibrium points coincide in the case of invex payoff functions. This is done on Hadamard manifolds, a particular case of noncompact Riemannian symmetric spaces. |
Cita | Ruiz Garzón, G., Osuna Gómez, R. y Rufián Lizana, A. (2020). Solutions of Optimization Problems on Hadamard Manifolds with Lipschitz Functions. Symmetry, 12 (804), 1-16. https://doi.org/10.3390/sym12050804. |
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