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An inexact conic bundle variant suited to column generation

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 0 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.
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https://hal.inria.fr/inria-00109402
Contributor : Claude Lemarechal Connect in order to contact the contributor
Submitted on : Wednesday, October 25, 2006 - 11:56:16 AM
Last modification on : Friday, June 26, 2020 - 4:56:01 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 8:50:20 PM

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  • HAL Id : inria-00109402, version 1

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Claude Lemarechal, Krzysztof Kiwiel. An inexact conic bundle variant suited to column generation. [Research Report] 2006. ⟨inria-00109402v1⟩

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