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Journal Articles Mathematical Programming Year : 2009

An inexact bundle variant suited to column generation

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Abstract

We give a bundle method for constrained convex optimization. Instead of using penalty functions, it shifts iterates towards feasibility, by way of a Slater point, assumed to be known. Besides, the method accepts an oracle delivering function and subgradient values with unknown accuracy. Our approach is motivated by a number of applications in column generation, in which constraints are positively homogeneous--so that zero is a natural Slater point--and an exact oracle may be time consuming. Finally, our convergence analysis employs arguments which have been little used so far in the bundle community. The method is illustrated on a number of cutting-stock problems.

Dates and versions

hal-00821373 , version 1 (09-05-2013)

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Krzysztof C. Kiwiel, Claude Lemaréchal. An inexact bundle variant suited to column generation. Mathematical Programming, 2009, 118 (1), pp.177-206. ⟨10.1007/s10107-007-0187-4⟩. ⟨hal-00821373⟩
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