Lagrangian Relaxation via Ballstep Subgradient Methods

Lagrangian Relaxation via Ballstep Subgradient Methods

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Article ID: iaor200954131
Country: United States
Volume: 32
Issue: 3
Start Page Number: 669
End Page Number: 686
Publication Date: Aug 2007
Journal: Mathematics of Operations Research
Authors: , ,
Keywords: programming: convex
Abstract:

We exhibit useful properties of ballstep subgradient methods for convex optimization using level controls for estimating the optimal value. Augmented with simple averaging schemes, they asymptotically find objective and constraint subgradients involved in optimality conditions. When applied to Lagrangian relaxation of convex programs, they find both primal and dual solutions, and have practicable stopping criteria. Up until now, similar results have only been known for proximal bundle methods, and for subgradient methods with divergent series stepsizes, whose convergence can be slow. Encouraging numerical results are presented for large–scale nonlinear multicommodity network flow problems.

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