Interior point methods for second-order cone programming and OR applications

Yu Ju Kuo, Hans Mittelmann

Research output: Contribution to journalArticle

41 Scopus citations

Abstract

Interior point methods (IPM) have been developed for all types of constrained optimization problems. In this work the extension of IPM to second order cone programming (SOCP) is studied based on the work of Andersen, Roos, and Terlaky. SOCP minimizes a linear objective function over the direct product of quadratic cones, rotated quadratic cones, and an affine set. It is described in detail how to convert several application problems to SOCP. Moreover, a proof is given of the existence of the step for the infeasible long-step path-following method. Furthermore, variants are developed of both long-step path-following and of predictor-corrector algorithms. Numerical results are presented and analyzed for those variants using test cases obtained from a number of application problems.

Original languageEnglish (US)
Pages (from-to)255-285
Number of pages31
JournalComputational Optimization and Applications
Volume28
Issue number3
DOIs
StatePublished - Sep 1 2004

Keywords

  • Interior point method
  • Operations research applications
  • Second-order core programming

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

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