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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Vydané v:Computational optimization and applications Ročník 60; číslo 2; s. 393 - 411
Hlavný autor: Jahn, Johannes
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Boston Springer US 01.03.2015
Springer Nature B.V
Predmet:
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
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Shrnutí: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