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An Inexact Conic Bundle Variant Suited to Column Generation
Subtitle:Raport Badawczy = Research Report ; RB/55/2006
Creator:Kiwiel, Krzysztof ; Lemarechal, Claude
Publisher:Instytut Badań Systemowych. Polska Akademia Nauk ; Systems Research Institute. Polish Academy of Sciences
Place of publishing: Date issued/created: Description:45 stron ; 21 cm ; Bibliografia s. 42-45
Subject and Keywords:Nondifferentiable optimization ; Optymalizacja niezróżnicowana ; Convex programming ; Programowanie wypukłe ; Proximal bundle methods ; Approximate subgradients ; Column generation ; Aproksymacja subgradientowa ; Generowanie kolumn ; Cutting-stock problem
Abstract:The paper presents a bundle method for constrained convex optimization. Instead of using penalty functions, it shifts iterates towards feasibility, by way of a SIater point, assumed to be known. Besides, the method accepts an oracle delivering function and subgradient vaIues with unknown accuracy. The proposed approach is motivated by a number of applications in column generation, in which constraints are positively homogeneous - so that 0 is a natural Slater point - and an exact oracle may be time consuming. Finally, this convergence analysis empIoys arguments which have been little used so far in the bundle community. The method is illustrated on a number of cutting-stock problems.
Relation:Raport Badawczy = Research Report
Resource type: Detailed Resource Type: Source: Language: Language of abstract: Rights:Licencja Creative Commons Uznanie autorstwa 4.0
Terms of use:Zasób chroniony prawem autorskim. [CC BY 4.0 Międzynarodowe] Korzystanie dozwolone zgodnie z licencją Creative Commons Uznanie autorstwa 4.0, której pełne postanowienia dostępne są pod adresem: ; -
Digitizing institution:Instytut Badań Systemowych Polskiej Akademii Nauk
Original in:Biblioteka Instytutu Badań Systemowych PAN
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