SDP reformulation for robust optimization problems based on nonconvex QP duality

Ryoichi Nishimura, Shunsuke Hayashi, Masao Fukushima

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


In a real situation, optimization problems often involve uncertain parameters. Robust optimization is one of distribution-free methodologies based on worst-case analyses for handling such problems. In this paper, we first focus on a special class of uncertain linear programs (LPs). Applying the duality theory for nonconvex quadratic programs (QPs), we reformulate the robust counterpart as a semidefinite program (SDP) and show the equivalence property under mild assumptions. We also apply the same technique to the uncertain second-order cone programs (SOCPs) with "single" (not side-wise) ellipsoidal uncertainty. Then we derive similar results on the reformulation and the equivalence property. In the numerical experiments, we solve some test problems to demonstrate the efficiency of our reformulation approach. Especially, we compare our approach with another recent method based on Hildebrand's Lorentz positivity.

Original languageEnglish
Pages (from-to)21-47
Number of pages27
JournalComputational Optimization and Applications
Issue number1
Publication statusPublished - 2013 May
Externally publishedYes


  • Nonconvex quadratic programming
  • Robust optimization
  • Second-order cone programming
  • Semidefinite programming

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics


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