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

Authors:
Hiroshi Konno;Naoya Kawadai;Hoang Tuy
Affiliations:
Department of Industrial and Systems Engineering, Chuo-University, Japan/;Department of Industrial Engineering and Management, Tokyo Institute of Technology, Japan/;Institute of Mathematics, Hanoi, Vietnam
Venue:
Journal of Global Optimization
Year:
2003

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Abstract

We will propose an outer-approximation (cutting plane) method for minimizing a function fX subject to semi-definite constraints on the variables X∈Rn. 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.