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Dynamic Subgradient Methods

Gregory Emiel (gregoryemiel***at***gmail.com)
Claudia Sagastizabal (sagastiz***at***impa.br)

Abstract: Lagrangian relaxation is commonly used to generate bounds for mixed-integer linear programming problems. However, when the number of dualized constraints is very large (exponential in the dimension of the primal problem), explicit dualization is no longer possible. In order to reduce the dual dimension, different heuristics were proposed. They involve a separation procedure to dynamically select a restricted set of constraints to be dualized along the iterations. This relax-and-cut type approach has shown its numerical efficiency in many combinatorial problems. We show Primal-dual convergence of such strategy when using an adapted subgradient method for the dual step.

Keywords: Subgradient Methods; Lagrangian Relaxation; Relax and Cut

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Integer Programming (Cutting Plane Approaches )

Citation: Instituto Nacional de Matem\'atica Pura e Aplicada, 2008

Download: [PDF]

Entry Submitted: 08/27/2008
Entry Accepted: 08/27/2008
Entry Last Modified: 12/04/2008

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