Extended reverse-convex programming: an approximate enumeration approach to global optimization

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• 作者：Gene A. Bunin
• 刊名：Journal of Global Optimization
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：65
• 期：2
• 页码：191-229
• 全文大小：2,070 KB
• 刊物类别：Business and Economics
• 刊物主题：Economics
  Operation Research and Decision Theory
  Computer Science, general
  Real Functions
  Optimization
  
• 出版者：Springer Netherlands
• ISSN：1573-2916
• 卷排序：65

文摘

A new approach to solving a large class of factorable nonlinear programming (NLP) problems to global optimality is presented in this paper. Unlike the traditional strategy of partitioning the decision-variable space employed in many branch-and-bound methods, the proposed approach approximates the NLP problem by a reverse-convex programming (RCP) problem to a controlled precision, with the latter then solved by an enumerative search. To establish the theoretical guarantees of the method, the notion of “RCP regularity” is introduced and it is proven that enumeration is guaranteed to yield a global optimum when the RCP problem is regular. An extended RCP algorithmic framework is then presented and its performance is examined for a small set of test problems.KeywordsReverse-convex programmingConcave programmingPiecewise-concave approximationFactorable programmingImplicit enumeration methods