Characterizations of set order relations and constrained set optimization problems via oriented distance function

Set-valued optimization problems are important and fascinating field of optimization theory and widely applied to image processing, viability theory, optimal control and mathematical economics. There are two types of criteria of solutions for the set-valued optimization problems: the vector criterio...

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Vydáno v:Optimization Ročník 66; číslo 11; s. 1741 - 1754
Hlavní autoři: Chen, Jiawei, Ansari, Qamrul Hasan, Yao, Jen-Chih
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Taylor & Francis 02.11.2017
Taylor & Francis LLC
Témata:
49J53
Cones
Constrained set optimization problems
Criteria
Economic models
Image processing
image space analysis
Mathematical programming
Nonlinear programming
Optimal control
optimality conditions
Optimization
oriented distance function
set order relations
Viability
ISSN:0233-1934, 1029-4945
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Shrnutí:Set-valued optimization problems are important and fascinating field of optimization theory and widely applied to image processing, viability theory, optimal control and mathematical economics. There are two types of criteria of solutions for the set-valued optimization problems: the vector criterion and the set criterion. In this paper, we adopt the set criterion to study the optimality conditions of constrained set-valued optimization problems. We first present some characterizations of various set order relations using the classical oriented distance function without involving the nonempty interior assumption on the ordered cones. Then using the characterizations of set order relations, necessary and sufficient conditions are derived for four types of optimal solutions of constrained set optimization problem with respect to the set order relations. Finally, the image space analysis is employed to study the c-optimal solution of constrained set optimization problems, and then optimality conditions and an alternative result for the constrained set optimization problem are established by the classical oriented distance function.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2017.1322082