Taiwanese Journal of Mathematics

Optimality and Duality on Riemannian Manifolds

Gabriel Ruiz-Garzón, Rafaela Osuna-Gómez, Antonio Rufián-Lizana, and Beatriz Hernández-Jiménez

Full-text: Open access

Abstract

Our goal in this paper is to translate results on function classes that are characterized by the property that all the Karush-Kuhn-Tucker points are efficient solutions, obtained in Euclidean spaces to Riemannian manifolds. We give two new characterizations, one for the scalar case and another for the vectorial case, unknown in this subject literature. We also obtain duality results and give examples to illustrate it.

Article information

Source
Taiwanese J. Math., Volume 22, Number 5 (2018), 1245-1259.

Dates
Received: 1 October 2017
Revised: 3 January 2018
Accepted: 6 May 2018
First available in Project Euclid: 21 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1526889714

Digital Object Identifier
doi:10.11650/tjm/180501

Mathematical Reviews number (MathSciNet)
MR3859374

Zentralblatt MATH identifier
06965417

Subjects
Primary: 90C29: Multi-objective and goal programming 53B21: Methods of Riemannian geometry 53C22: Geodesics [See also 58E10] 58E10: Applications to the theory of geodesics (problems in one independent variable) 80M50: Optimization

Keywords
generalized convexity Riemannian manifolds efficient solutions duality

Citation

Ruiz-Garzón, Gabriel; Osuna-Gómez, Rafaela; Rufián-Lizana, Antonio; Hernández-Jiménez, Beatriz. Optimality and Duality on Riemannian Manifolds. Taiwanese J. Math. 22 (2018), no. 5, 1245--1259. doi:10.11650/tjm/180501. https://projecteuclid.org/euclid.twjm/1526889714


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