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Journal of Global Optimization

, Volume 25, Issue 2, pp 141–155 | Cite as

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

  • Hiroshi Konno
  • Naoya Kawadai
  • Hoang Tuy
Article

Abstract

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.

Semi-definite programming Low rank nonconvex problem Cutting plane algorithm Outer-approximation Semi-infinite programming Ellipsoidal separation Quadratic regression Semi-definite logit model 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Hiroshi Konno
    • 1
  • Naoya Kawadai
    • 2
  • Hoang Tuy
    • 3
  1. 1.Department of Industrial and Systems EngineeringChuo-UniversityJapan
  2. 2.Department of Industrial Engineering and ManagementTokyo Institute of TechnologyJapan
  3. 3.Institute of MathematicsHanoiVietnam

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