Generalized Bundle Methods for Sum-Functions with ''Easy'' Components: Applications to Multicommodity Network Design

Frangioni, Antonio and Gorgone, Enrico (2011) Generalized Bundle Methods for Sum-Functions with ''Easy'' Components: Applications to Multicommodity Network Design. Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

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Abstract

We propose a modification to the (generalized) bundle scheme for minimization of a convex nondifferentiable sum-function in the case where some of the components are ''easy'', that is, they are Lagrangian functions of explicitly known convex programs with ''few'' variables and constraints. This happens in many practical cases, particularly within applications to combinatorial optimization. In this case one can insert in the master problem a suitably modified representation of the original convex subproblem, as an alternative to iteratively inner-approximating it by means of the produced extreme points, thus providing the algorithm with exact information about a part of the objective function, possibly leading to performance improvements. This is shown to happen in at least one relevant application: the computation of tight lower bounds for Fixed-Charge Multicommodity Min-Cost Flow problems.

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