Ergodic, primal convergence in dual subgradient schemes for convex programming

Ergodic, primal convergence in dual subgradient schemes for convex programming

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Article ID: iaor20003730
Country: Germany
Volume: 50
Issue: 2
Start Page Number: 283
End Page Number: 312
Publication Date: Jan 1999
Journal: Mathematical Methods of Operations Research (Heidelberg)
Authors: , ,
Keywords: Lagrangean methods
Abstract:

Lagrangean dualization and subgradient optimization techniques are frequently used within the field of computational optimization for finding approximate solutions to large, structured optimization problems. The dual subgradient scheme does not automatically produce primal feasible solutions; there is an abundance of techniques for computing such solutions (via penalty functions, tangential approximation schemes, or the solution of auxiliary primal programs), all of which require a fair amount of computational effort. We consider a subgradient optimization scheme applied to a Lagrangean dual formulation of a convex program, and construct, at minor cost, an ergodic sequence of subproblem solutions which converges to the primal solution set. Numerical experiments performed on a traffic equilibrium assignment problem under road pricing show that the computation of the ergodic sequence results in a considerable improvement in the quality of the primal solutions obtained, compared to those generated in the basic subgradient scheme.

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