Preprint Article Version 1 This version is not peer-reviewed

Optimality Conditions for Vector Equilibrium Problems on Hadamard Manifolds

Version 1 : Received: 11 July 2019 / Approved: 15 July 2019 / Online: 15 July 2019 (05:30:05 CEST)

A peer-reviewed article of this Preprint also exists.

Ruiz-Garzón, G.; Osuna-Gómez, R.; Ruiz-Zapatero, J. Necessary and Sufficient Optimality Conditions for Vector Equilibrium Problems on Hadamard Manifolds. Symmetry 2019, 11, 1037. Ruiz-Garzón, G.; Osuna-Gómez, R.; Ruiz-Zapatero, J. Necessary and Sufficient Optimality Conditions for Vector Equilibrium Problems on Hadamard Manifolds. Symmetry 2019, 11, 1037.

Journal reference: Symmetry 2019, 11, 1037
DOI: 10.3390/sym11081037

Abstract

The aim of this paper is to obtain Karush-Kuhn-Tucker optimality conditions for weakly efficient solutions to vector equilibrium problems with the addition of constraints in the novel context of Hadamard manifolds as opposed to the classical examples of Banach, normed or Hausdorff spaces. More specifically, classical necessary and sufficient conditions for weakly efficient solutions to the constrained vector optimization problem are presented. As well as some examples. The results presented in this paper generalize results obtained by Gong (2008) and Wei and Gong (2010) and Feng and Qiu (2014) from Hausdorff topological vector spaces, real normed spaces and real Banach spaces to Hadamard manifolds, respectively.

Subject Areas

vector equilibrium problem; generalized convexity; Hadamard manifolds; weakly efficient solutions

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