A Steepest Descent-Like Method for Variable Order Vector Optimization Problems

In some applications, the comparison between two elements may depend on the point leading to the so called variable order structure. Optimality concepts may be extended to this more general framework. In this paper, we extend the steepest descent-like method for smooth unconstrained vector optimizat...

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Bibliographic Details
Published inJournal of optimization theory and applications Vol. 162; no. 2; pp. 371 - 391
Main Authors Bello Cruz, J. Y., Bouza Allende, G.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.08.2014
Springer Nature B.V
Subjects
Algorithms
Analysis
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Engineering
Mathematical analysis
Mathematics
Mathematics and Statistics
Medical diagnosis
Operations Research/Decision Theory
Optimization
Sequences
Studies
Theory of Computation
Vectors (mathematics)
Gradient-like method
Convexity
Variable order
Vector optimization
Weakly efficient points
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ISSN0022-3239
1573-2878
DOI10.1007/s10957-013-0308-6

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Summary:In some applications, the comparison between two elements may depend on the point leading to the so called variable order structure. Optimality concepts may be extended to this more general framework. In this paper, we extend the steepest descent-like method for smooth unconstrained vector optimization problems under a variable order structure. Roughly speaking, we see that every accumulation point of the generated sequence satisfies a necessary first order condition. We discuss the consequence of this fact in the convex case.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-013-0308-6