Simplex-type algorithm for second-order cone programmes via semi-infinite programming reformulation

Shunsuke Hayashi, Takayuki Okuno, Yoshihiko Ito

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

To solve the (linear) second-order cone programmes (SOCPs), the primal–dual interior-point method has been studied extensively so far and said to be the most efficient method by many researchers. On the other hand, the simplex-type method for SOCP is much less spotlighted, while it still keeps an important position for linear programmes. In this paper, we apply the dual–simplex primal-exchange (DSPE) method, which was originally developed for solving linear semi-infinite programmes, to the SOCP by reformulating the second-order cone constraint as an infinite number of linear inequality constraints. Then, we show that the sequence generated by the DSPE method converges to the SOCP optimum under certain assumptions. In the numerical experiments, we consider the situation to solve multiple SOCPs with similar structures successively. Then we observe that our simplex-type method can be more efficient than the existing interior-point method when we apply the so-called ‘hot start’ technique.

Original languageEnglish
Pages (from-to)1272-1297
Number of pages26
JournalOptimization Methods and Software
Volume31
Issue number6
DOIs
Publication statusPublished - 2016 Nov 1

Keywords

  • linear semi-infinite programme
  • second-order cone programme
  • simplex method

ASJC Scopus subject areas

  • Software
  • Control and Optimization
  • Applied Mathematics

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