A Regularized Explicit Exchange Method for Semi-Infinite Programs with an Infinite Number of Second-Order Cone Constraints
The semi-infinite program (SIP) is normally represented with infinitely many inequality constraints, and has been much studied so far. However, there have been only a few studies on the SIP involving second-order cone (SOC) constraints, even though it has important applications such as Chebychev-like approximation and filter design.In this paper, we focus on the SIP with a convex objective function and infinitely many SOC constraints, called the SISOCP for short. We show that, under a generalized Slater constraint qualification, an optimum of the SISOCP satisfies the KKT conditions that can be represented with only a finite subset of the SOC constraints. Next we introduce the regularization and the explicit exchange methods for solving the SISOCP. We first provide an explicit exchange method without a regularization technique, and show that it has global convergence under the strict convexity assumption on the objective function. Then we propose an algorithm combining a regularization method with the explicit exchange method. For the SISOCP, we establish global convergence of the hybrid algorithm without the strict convexity assumption.
Takayuki Okuno Shunsuke Hayashi Masao Fukushima
Department of Applied Mathematics and Physics, Graduate School of Informatics,Kyoto University, Kyoto 606-8501, JAPAN
国际会议
上海
英文
92-93
2010-12-10（万方平台首次上网日期，不代表论文的发表时间）