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

Gabriel Ruiz-Garzón, Rafaela Osuna-Gómez, Antonio Rufián-Lizana and Beatriz Hernández-Jiménez
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Gabriel Ruiz-Garzón: Instituto de Desarrollo Social y Sostenible (INDESS), Universidad de Cádiz, 11003 Cádiz, Spain
Rafaela Osuna-Gómez: Departamento de Estadística e I.O., Universidad de Sevilla, 41004 Sevilla, Spain
Antonio Rufián-Lizana: Departamento de Estadística e I.O., Universidad de Sevilla, 41004 Sevilla, Spain
Beatriz Hernández-Jiménez: Departamento de Economía, Métodos Cuantitativos e Historia Económica, Universidad Pablo de Olavide, 41013 Sevilla, Spain

Mathematics, 2020, vol. 8, issue 12, 1-19

Abstract: 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.

Keywords: generalized convexity; Hadamard manifold; approximate efficient solution; Stackelberg equilibrium point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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