Journal of Scientific Computing

, Volume 68, Issue 2, pp 573–595 | Cite as

Computation Algorithm for Convex Semi-infinite Program with Second-Order Cones: Special Analyses for Affine and Quadratic Case

  • Shunsuke Hayashi
  • Soon-Yi WuEmail author
  • Liping Zhang


We focus on the convex semi-infinite program with second-order cone constraints (for short, SOCCSIP), which has wide applications such as filter design, robust optimization, and so on. For solving the SOCCSIP, we propose an explicit exchange method, and prove that the algorithm terminates in a finite number of iterations. In the convergence analysis, we do not need to use the special structure of second-order cone (SOC) when the objective or constraint function is strictly convex. However, if both of them are non-strictly convex and constraint function is affine or quadratic, then we have to utilize the SOC complementarity conditions and the spectral factorization techniques associated with Euclidean Jordan algebra. We also show that the obtained output is an approximate optimum of SOCCSIP. We report some numerical results involving the application to the robust optimization in the classical convex semi-infinite program.


Continuous optimization Semi-infinite program Exchange method Second-order cone 

Mathematics Subject Classification

90C30 90C33 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Graduate School of Information SciencesTohoku UniversitySendaiJapan
  2. 2.Department of MathematicsNational Cheng Kung UniversityTainanTaiwan
  3. 3.National Center for Theoretical SciencesTainanTaiwan
  4. 4.Department of Mathematical SciencesTsinghua UniversityBeijingChina

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