We propose a discretization algorithm for solving a class of nonsmooth convex semi-infinite programming problems that is based on a bundle method. Instead of employing the inexact calculation to evaluate the lower level problem, we shall carry out a discretization scheme. The discretization method is used to get a number of discretized problems which are solved by the bundle method. In particular, the subproblem used to generate a new point is independent of the number of constraints of the discretized problem. We apply a refinement-step which can be used to guarantee the convergence of the bundle method for the discretized problems as well as reduce the cost of the evaluations for the constraint functions during iteration. In addition we adopt an aggregation technique to manage the bundle information coming from previous steps. Both theoretical convergence analysis and preliminary computational results are reported. The results obtained have shown the good performance of the new algorithm.

中文翻译：

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基于束方法的非光滑凸半无限规划问题的离散化算法

我们提出一种基于束方法的离散化算法来解决一类非光滑凸半无限规划问题。代替使用不精确的计算来评估较低级别的问题，我们将执行离散化方案。离散化方法用于获得许多离散问题，这些问题可以通过捆绑方法解决。特别是，用于生成新点的子问题与离散问题的约束数量无关。我们应用了一个改进步骤，该步骤可用于确保离散方法的束方法收敛，并减少迭代过程中约束函数的评估成本。另外，我们采用一种聚合技术来管理来自先前步骤的捆绑信息。理论收敛性分析和初步计算结果均已报道。获得的结果表明了新算法的良好性能。