Asymptotic strong duality for bounded integer programming: A logarithmic-exponential dual formulation

• 成果类型: Article
• 署名作者: Sun, XL; Li, D
• 署名单位: Shanghai University; Chinese University of Hong Kong
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.25.4.625.12114
• 发表日期: 2000
• 页码: 625-644
• 关键词: nonconvex optimization problems; global optimization; system-reliability; gap

摘要

A logarithmic-exponential dual formulation is proposed in this paper for bounded integer programming problems. This new dual formulation possesses an asymptotic strong duality property and guarantees the identification of an optimal solution of the primal problem. These prominent features are achieved by exploring a novel nonlinear Lagrangian function, deriving an asymptotic zero duality gap, investigating the unimodality of the associated dual function and ensuring the primal feasibility of optimal solutions in the dual formulation. One other feature of the logarithmic-exponential dual formulation is that no actual dual search is needed when parameters are set above certain threshold-values.