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

Antonio Frangioni(frangio***at***di.unipi.it)
Enrico Gorgone(egorgone***at***deis.unical.it)

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.

Keywords: Nondifferentiable Optimization, Bundle methods, Lagrangian Relaxation, Partial Dantzig-Wolfe Decomposition, Multicommodity Network Design

Category 1: Convex and Nonsmooth Optimization

Category 2: Linear, Cone and Semidefinite Programming (Linear Programming )

Category 3: Network Optimization

Citation: Technical Report 11-08, Dipartimento di Informatica, Universit\`a di Pisa

Download: [PDF]

Entry Submitted: 06/03/2011
Entry Accepted: 06/03/2011
Entry Last Modified: 06/03/2011

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