Journal of Global Optimization

, Volume 60, Issue 1, pp 25–48 | Cite as

Local reduction based SQP-type method for semi-infinite programs with an infinite number of second-order cone constraints



The second-order cone program (SOCP) is an optimization problem with second-order cone (SOC) constraints and has achieved notable developments in the last decade. The classical semi-infinite program (SIP) is represented with infinitely many inequality constraints, and has been studied extensively so far. In this paper, we consider the SIP with infinitely many SOC constraints, called the SISOCP for short. Compared with the standard SIP and SOCP, the studies on the SISOCP are scarce, even though it has important applications such as Chebychev approximation for vector-valued functions. For solving the SISOCP, we develop an algorithm that combines a local reduction method with an SQP-type method. In this method, we reduce the SISOCP to an SOCP with finitely many SOC constraints by means of implicit functions and apply an SQP-type method to the latter problem. We study the global and local convergence properties of the proposed algorithm. Finally, we observe the effectiveness of the algorithm through some numerical experiments.


Semi-infinite programming Second-order cone constraints SQP-type method Local reduction method 



We would like to thank two anonymous referees for their valuable comments and suggestions.


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Management Science, Faculty of EngineeringDivision I, Tokyo University of ScienceTokyoJapan
  2. 2.Department of Information Systems and Mathematical Science, Faculty of Information System and EngineeringNanzan UniversityAichiJapan

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