Lagrangian relaxation via ballstep subgradient methods

• 成果类型: Article
• 署名作者: Kiwiel, Krzysztof C.; Larsson, Torbjoern; Lindberg, P. O.
• 署名单位: Polish Academy of Sciences; Systems Research Institute of the Polish Academy of Sciences; Linkoping University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1070.0261
• 发表日期: 2007
• 页码: 669-686
• 关键词: bundle methods; volume algorithm; primal solutions; optimization; CONVERGENCE; EFFICIENCY; DECOMPOSITION

摘要

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.