Bitte verwenden Sie diesen Link, um diese Publikation zu zitieren, oder auf sie als Internetquelle zu verweisen: https://hdl.handle.net/10419/312239 
Erscheinungsjahr: 
2022
Quellenangabe: 
[Journal:] Mathematical Methods of Operations Research [ISSN:] 1432-5217 [Volume:] 96 [Issue:] 1 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2022 [Pages:] 39-82
Verlag: 
Springer, Berlin, Heidelberg
Zusammenfassung: 
This article introduces the new class of continuous set covering problems. These optimization problems result, among others, from product portfolio design tasks with products depending continuously on design parameters and the requirement that the product portfolio satisfies customer specifications that are provided as a compact set. We show that the problem can be formulated as semi-infinite optimization problem (SIP). Yet, the inherent non-smoothness of the semi-infinite constraint function hinders the straightforward application of standard methods from semi-infinite programming. We suggest an algorithm combining adaptive discretization of the infinite index set and replacement of the non-smooth constraint function by a two-parametric smoothing function. Under few requirements, the algorithm converges and the distance of a current iterate can be bounded in terms of the discretization and smoothing error. By means of a numerical example from product portfolio optimization, we demonstrate that the proposed algorithm only needs relatively few discretization points and thus keeps the problem dimensions small.
Schlagwörter: 
Semi-infinite programming
Continuous set covering
Product portfolio optimization
Mathematical modelling
Optimization
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