A derivative-free descent method in set optimization

Based on a vectorization result in set optimization with respect to the set less order relation, this paper shows how to relate two nonempty sets on a computer. This result is developed for generalized convex sets and polyhedral sets in finite dimensional spaces. Using this approach a numerical meth...

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Bibliographic Details
Published in:Computational optimization and applications Vol. 60; no. 2; pp. 393 - 411
Main Author: Jahn, Johannes
Format: Journal Article
Language:English
Published: Boston Springer US 01.03.2015
Springer Nature B.V
Subjects:
Analysis
Computation
Computational geometry
Computer science
Computer simulation
Convex and Discrete Geometry
Descent
Management Science
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Numerical analysis
Operations Research
Operations Research/Decision Theory
Optimization
Set theory
Statistics
Studies
Vector processing (computers)
90C29
Set less order relation
06A06
Vectorization
90C56
Set optimization
ISSN:0926-6003, 1573-2894
Online Access:Get full text
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Summary:Based on a vectorization result in set optimization with respect to the set less order relation, this paper shows how to relate two nonempty sets on a computer. This result is developed for generalized convex sets and polyhedral sets in finite dimensional spaces. Using this approach a numerical method for the determination of optimal scenarios is presented. A new derivative-free descent method for the solution of set optimization problems is given together with numerical results in low dimensions.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-014-9674-8