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Inner Parallel Sets in Mixed-Integer Optimization

Neumann, Christoph


This thesis contains an extensive study of inner parallel sets in mixed-integer optimization. Inner parallel sets are a recent idea in this context and offer a possibility to relax the difficulties imposed by integrality constraints by guaranteeing feasibility of roundings of their (continuous) elements. To be able to use inner parallel sets algorithmically, various modifications, such as their enlargements and inner and outer approximations, are helpful and sometimes even necessary. Such ideas are introduced and investigated in this thesis, both theoretically as well as computationally.

From our theoretical study of inner parallel sets emerge a number of feasible rounding approaches which mainly focus on the computation of good feasible points for mixed-integer linear and nonlinear minimization problems. Good feasible points are useful in the context of solving these problems by providing tight upper bounds on the objective value. In especially difficult cases, feasible rounding approaches may also be considered as an alternative to solving a problem.

The contributions of this thesis include a thorough discussion of possibilities to enlarge inner parallel sets in the linear as well as in the nonlinear setting. ... mehr

Volltext §
DOI: 10.5445/IR/1000135848
Veröffentlicht am 02.08.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Operations Research (IOR)
Publikationstyp Hochschulschrift
Publikationsdatum 02.08.2021
Sprache Englisch
Identifikator KITopen-ID: 1000135848
Verlag Karlsruher Institut für Technologie (KIT)
Umfang xi, 137 S.
Art der Arbeit Dissertation
Fakultät Fakultät für Wirtschaftswissenschaften (WIWI)
Institut Institut für Operations Research (IOR)
Prüfungsdatum 22.07.2021
Schlagwörter optimization, cutting plane, inner parallel set
Referent/Betreuer Stein, O.
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