Approximate Efficient Solutions of the Vector Optimization Problem on Hadamard Manifolds via Vector Variational Inequalities

This article has two objectives. Firstly, we use the vector variational-like inequalities problems to achieve local approximate (weakly) efficient solutions of the vector optimization problem within the novel field of the Hadamard manifolds. Previously, we introduced the concepts of generalized appr...

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Detalles Bibliográficos
Autores: Ruiz Garzón, Gabriel, Osuna Gómez, Rafaela, Rufián Lizana, Antonio, Hernández Jiménez, Beatriz
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/104542
Acceso en línea:https://hdl.handle.net/11441/104542
https://doi.org/10.3390/math8122196
Access Level:acceso abierto
Palabra clave:generalized convexity
Hadamard manifold
approximate efficient solution
Stackelberg equilibrium point
Descripción
Sumario:This article has two objectives. Firstly, we use the vector variational-like inequalities problems to achieve local approximate (weakly) efficient solutions of the vector optimization problem within the novel field of the Hadamard manifolds. Previously, we introduced the concepts of generalized approximate geodesic convex functions and illustrated them with examples. We see the minimum requirements under which critical points, solutions of Stampacchia, and Minty weak variational-like inequalities and local approximate weakly efficient solutions can be identified, extending previous results from the literature for linear Euclidean spaces. Secondly, we show an economical application, again using solutions of the variational problems to identify Stackelberg equilibrium points on Hadamard manifolds and under geodesic convexity assumptions.