Newton-like methods for efficient solutions in vector optimization

Authors:
Thai Doan Chuong
Affiliations:
Department of Mathematics & Applications, Saigon University, Hochiminh City, Vietnam
Venue:
Computational Optimization and Applications
Year:
2013

Citing 6
Cited 0

A Projected Gradient Method for Vector Optimization Problems

Computational Optimization and Applications
Proximal Methods in Vector Optimization

SIAM Journal on Optimization
Multicriteria Optimization

Multicriteria Optimization
On the choice of parameters for the weighting method in vector optimization

Mathematical Programming: Series A and B
Newton's Method for Multiobjective Optimization

SIAM Journal on Optimization
A steepest descent method for vector optimization

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this work we study the Newton-like methods for finding efficient solutions of the vector optimization problem for a map from a finite dimensional Hilbert space X to a Banach space Y, with respect to the partial order induced by a closed, convex and pointed cone C with a nonempty interior. We present both exact and inexact versions, in which the subproblems are solved approximately, within a tolerance. Furthermore, we prove that under reasonable hypotheses, the sequence generated by our method converges to an efficient solution of this problem.