Sparse second order cone programming formulations for convex optimization problems

Kazuhiro Kobayashi, Sunyoung Kim, Masakazu Kojima

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Second order cone program (SOCP) formulations of convex optimization problems are studied. We show that various SOCP formulations can be obtained depending on how auxiliary variables are introduced. An efficient SOCP formulation that increases the computational efficiency is presented by investigating the relationship between the sparsity of an SOCP formulation and the sparsity of the Schur complement matrix. Numerical results of selected test problems using SeDuMi and LANCELOT are included to demonstrate the performance of the SOCP formulation.

Original languageEnglish
Pages (from-to)241-264
Number of pages24
JournalJournal of the Operations Research Society of Japan
Issue number3
StatePublished - Sep 2008


  • Convex optimization problem
  • Correlative sparsity
  • Optimization
  • Primal-dual interior-point method
  • Second-order cone program
  • The Schur complement matrix


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