Cutting Plane Algorithms for Nonlinear Semi-Definite Programming Problems with Applications

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• 作者：Hiroshi Konno ; Naoya Kawadai and Hoang Tuy
• 关键词：Semi ; definite programming ; Low rank nonconvex problem ; Cutting plane algorithm ; Outer ; approximation ; Semi ; infinite programming ; Ellipsoidal separation ; Quadratic regression ; Semi ; definite logit model
• 刊名：Journal of Global Optimization
• 出版年：2003
• 出版时间：2003
• 年：2003
• 卷：25
• 期：2
• 页码：141-155
• 全文大小：244 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

文摘

We will propose an outer-approximation (cutting plane) method for minimizing a function fX subject to semi-definite constraints on the variables XRn. A number of efficient algorithms have been proposed when the objective function is linear. However, there are very few practical algorithms when the objective function is nonlinear. An algorithm to be proposed here is a kind of outer-approximation(cutting plane) method, which has been successfully applied to several low rank global optimization problems including generalized convex multiplicative programming problems and generalized linear fractional programming problems, etc. We will show that this algorithm works well when f is convex and n is relatively small. Also, we will provide the proof of its convergence under various technical assumptions.