A Potential Reduction Algorithm Allowing Column Generation

本研究的目标是根据分析中心及其相关势函数的最新结果开发一种潜在约简算法，该算法(1)允许列生成，(2)其复杂性不依赖于完整的约束系统，(3)可实现实际效率。这种类型的技术为解决诸如半无限规划、凸非线性规划和组合优化问题等优化规划提供了很大的灵活性，其中约束数量非常大或某些约束不明确已知。

The goal of this research is to develop a potential reduction algorithm, based on recent results for analytic centers and their associated potential functions, that (1) allows column generation, (2) whose complexity does not depend on the full system of constraints and (3) that is implementable with practical efficiency. This type of a technique permits a great deal of flexibility for solving such optimization programs as semi-infinite programs, convex nonlinear programs and combinatorial optimization problems, in which the number of constraints is very large or some constraints are not explicitly known.