Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/288614 
Year of Publication: 
2020
Citation: 
[Journal:] Journal of Global Optimization [ISSN:] 1573-2916 [Volume:] 78 [Issue:] 1 [Publisher:] Springer US [Place:] New York, NY [Year:] 2020 [Pages:] 37-47
Publisher: 
Springer US, New York, NY
Abstract: 
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.
Subjects: 
Global optimization
D.c. programming
Multi-objective linear programming
Linear vector optimization
JEL: 
C26
C29
B55
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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