Generalized Proximal Method for Efficient Solutions in Vector Optimization

This article is devoted to developing the generalized proximal algorithm of finding efficient solutions to the vector optimization problem for a mapping from a uniformly convex and uniformly smooth Banach space to a real Banach space with respect to the partial order induced by a pointed closed conv...

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Vydáno v:Numerical functional analysis and optimization Ročník 32; číslo 8; s. 843 - 857
Hlavní autor: Chuong, T. D.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia, PA Taylor & Francis Group 01.08.2011
Taylor & Francis
Témata:
Algorithms
Banach space
Calculus of variations and optimal control
Efficient solution
Exact sciences and technology
Functional analysis
Generalized proximal method
Mapping
Mathematical analysis
Mathematical models
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Optimization
Sciences and techniques of general use
Uniformly convex
Uniformly smooth
Vector optimization
Vectors (mathematics)
Generalized proximal method
65K05
Efficient solution
Uniformly smooth
Optimization method
Banach space
Algorithm
Weak convergence
Numerical analysis
49J52
90C25
Ordering
Variational calculus
Uniformly convex
Vector optimization
Mathematical programming
49M99
ISSN:0163-0563, 1532-2467
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Popis
Shrnutí:This article is devoted to developing the generalized proximal algorithm of finding efficient solutions to the vector optimization problem for a mapping from a uniformly convex and uniformly smooth Banach space to a real Banach space with respect to the partial order induced by a pointed closed convex cone. In contrast to most published literature on this subject, our algorithm does not depend on the nonemptiness of ordering cone of the space under consideration and deals with finding efficient solutions of the vector optimization problem in question. We prove that under some suitable conditions the sequence generated by our method weakly converges to an efficient solution of this problem.
Bibliografie:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0163-0563
1532-2467
DOI:10.1080/01630563.2011.587072