Generalized Proximal Method for Efficient Solutions in Vector Optimization

2011 ◽  
Vol 32 (8) ◽  
pp. 843-857 ◽  
Author(s):  
T. D. Chuong
Keyword(s):  
Vector Optimization ◽  
Efficient Solutions ◽  
Proximal Method

An interior proximal method in vector optimization

2011 ◽  
Vol 214 (3) ◽  
pp. 485-492 ◽  
Author(s):  
Kely D.V. Villacorta ◽  
P. Roberto Oliveira
Keyword(s):  
Vector Optimization ◽  
Proximal Method

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

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2196
Author(s):  
Gabriel Ruiz-Garzón ◽  
Rafaela Osuna-Gómez ◽  
Antonio Rufián-Lizana ◽  
Beatriz Hernández-Jiménez
Keyword(s):  
Vector Optimization ◽  
Optimization Problem ◽  
Equilibrium Points ◽  
Variational Problems ◽  
Efficient Solutions ◽  
Vector Optimization Problem ◽  
Stackelberg Equilibrium ◽  
Hadamard Manifolds ◽  
Geodesic Convexity ◽  
Weakly Efficient Solutions

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.

scholarly journals A property of efficient and ε-efficient solutions in vector optimization

2005 ◽  
Vol 18 (4) ◽  
pp. 409-414 ◽  
Author(s):  
César Gutiérrez ◽  
Bienvenido Jiménez ◽  
Vicente Novo
Keyword(s):  
Vector Optimization ◽  
Efficient Solutions

Existence of weakly efficient solutions in nonsmooth vector optimization

2008 ◽  
Vol 200 (2) ◽  
pp. 547-556 ◽  
Author(s):  
Lucelina Batista Santos ◽  
Marko Rojas-Medar ◽  
Gabriel Ruiz-Garzón ◽  
Antonio Rufián-Lizana
Keyword(s):  
Vector Optimization ◽  
Efficient Solutions ◽  
Weakly Efficient Solutions ◽  
Nonsmooth Vector Optimization
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