非光滑约束优化基于非精确数据的改进水平束方法

A Modified Level Bundle Method with Inexact Data for Nonsmooth Constrained Optimization

本文提出了一个求解非光滑约束优化问题基于非精确数据的改进水平束方法。该方法引入了非精确数据及相应的近似改进函数。此外,通过在投影子问题中引入Bregman距离以代替传统的欧氏距离,从而可以充分利用可行集的几何集合,减少算法的计算量。最后证明了算法的全局收敛性并分析了迭代复杂度。

This paper presents a modified level bundle method with inexact data for nonsmooth constrained optimization.In the method,the inexact data and the approximate improvement function are in-troduced.Moreover,in the projection subproblem,the Bregman distance is used to replace the classical Euclidean distance,in order that the geometric structure of the feasible set can be taken into account,which can reduce the computation of the algorithm.Global convergence of the algo-rithm is proved and the iterative complexity is analyzed.