A Newton-like method for variable order vector optimization problems
type: Item
instance of: scholarly article
title: A Newton-like method for variable order vector optimization problems
zbMATH Open document ID: 1403.90592
author: G. Bouza Allende
author: Yuri Rafael Leite Pereira
author: Glaydston~de Carvalho Bento
published in: Journal of Optimization Theory and Applications
publication date: 2018-06-08T00:00:00Z
review text: The convexity and strong convexity with respect to a mapping are introduced in the class of vector functions defined on an \(n\)-dimensional non-empty open and convex set. The relation between the critical points of a convex, respectively strongly convex vector function and weakly efficient points, respectively efficient points is studied. Newton's method is extended for minimizing a strongly convex vector function with respect to a variable order, using a quadratic approximation of the scalarized convex function. The existence and the uniqueness of the solution is proved and properties of Newton's direction are obtained: the characterization of efficiency, the continuity of the direction, upper bounds and the descent of the objective functions. The algorithm converges. The convergence rate of the sequence generated by Newton's method for a variable order vector optimization is analyzed.
reviewed by: Gabriela Cristescu
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 26B25
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 6882327
zbMATH Keywords: descent direction
zbMATH Keywords: efficient points
zbMATH Keywords: \(K\)-strong convexity
zbMATH Keywords: Newton method
zbMATH Keywords: variable order vector optimization
MaRDI profile type: Publication
full work available at URL: s10957-018-1236-2
OpenAlex ID: W2793229727
cites work: Domination structures and multicriteria problems in N-person games
cites work: Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives
cites work: Q4461359
cites work: Multicriteria Optimization
cites work: Advancing equitability in multiobjective programming
cites work: Variable preference modeling with ideal-symmetric convex cones
cites work: Advances in Cone-Based Preference Modeling for Decision Making with Multiple Criteria
cites work: Optimal elements in vector optimization with a variable ordering structure
cites work: Optimality conditions for vector optimization problems with variable ordering structures
cites work: Variable Ordering Structures in Vector Optimization
cites work: Characterization of approximate solutions of vector optimization problems with a variable order structure
cites work: Concepts for approximate solutions of vector optimization problems with variable order structures
cites work: Fixed points and variational principles with applications to capability theory of wellbeing via variational rationality
cites work: Variational analysis in psychological modeling
cites work: Convergence for vector optimization problems with variable ordering structure
cites work: A steepest descent-like method for variable order vector optimization problems
cites work: Newton's Method for Multiobjective Optimization
cites work: A quadratically convergent Newton method for vector optimization
cites work: Q5555984
cites work: Q4830373
cites work: Nonlinear multiobjective optimization
cites work: Trust region globalization strategy for the nonconvex unconstrained multiobjective optimization problem
cites work: A trust-region method for unconstrained multiobjective problems with applications in satisficing processes
DOI: 10.1007/S10957-018-1236-2
Wikidata QID: Q130194366
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description: scientific article; zbMATH DE number 6882327