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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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Submitted on : Friday, November 10, 2006 - 9:59:28 AM
Last modification on : Monday, November 23, 2020 - 12:52:03 PM
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  • HAL Id : inria-00109402, version 2




Krzysztof Kiwiel, Claude Lemarechal. An inexact conic bundle variant suited to column generation. [Research Report] RR-6011, INRIA. 2006. ⟨inria-00109402v2⟩



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