Solving polyhedral d.c. optimization problems via concave minimization

The problem of minimizing the difference of two convex functions is called polyhedral d.c. optimization problem if at least one of the two component functions is polyhedral. We characterize the existence of global optimal solutions of polyhedral d.c. optimization problems. This result is used to sho...

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Vydáno v:Journal of global optimization Ročník 78; číslo 1; s. 37 - 47
Hlavní autoři: vom Dahl, Simeon, Löhne, Andreas
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY Springer US 01.09.2020
Springer
Springer Nature B.V
Témata:
Algorithms
Computer Science
D.c. programming
Global optimization
Linear vector optimization
Mathematics
Mathematics and Statistics
Multi-objective linear programming
Operations Research/Decision Theory
Optimization
Real Functions
Global optimization
D.c. programming
52B55
90C29
Linear vector optimization
90C26
Multi-objective linear programming
ISSN:1573-2916, 0925-5001, 1573-2916
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Shrnutí:The problem of minimizing the difference of two convex functions is called polyhedral d.c. optimization problem if at least one of the two component functions is polyhedral. We characterize the existence of global optimal solutions of polyhedral d.c. optimization problems. This result is used to show that, whenever the existence of an optimal solution can be certified, polyhedral d.c. optimization problems can be solved by certain concave minimization algorithms. No further assumptions are necessary in case of the first component being polyhedral and just some mild assumptions to the first component are required for the case where the second component is polyhedral. In case of both component functions being polyhedral, we obtain a primal and dual existence test and a primal and dual solution procedure. Numerical examples are discussed.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:1573-2916
0925-5001
1573-2916
DOI:10.1007/s10898-020-00913-z