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

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...

Full description

Saved in:
Bibliographic Details
Published inJournal of global optimization Vol. 25; no. 2; pp. 141 - 155
Main Authors Konno, Hiroshi, Kawadai, Naoya, Tuy, Hoang
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Nature B.V 01.02.2003
Subjects
Algorithms
Approximation
Discriminant analysis
Eigenvalues
Linear programming
Optimization
Online AccessGet full text
ISSN0925-5001
1573-2916
DOI10.1023/A:1021985014197

Cover

More Information
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0925-5001
1573-2916
DOI:10.1023/A:1021985014197