非光滑约束优化的改进水平束方法

An improved level bundle method for nonsmooth constrained optimization

为求解一类非光滑约束凸优化问题,提出了基于Bregman距离的水平束方法,将传统欧氏距离推广到广义Bregman距离,从而可充分利用可行集的几何结构,提升计算效率。该方法利用多面体模型近似原问题的目标函数和约束函数,并引入改进函数作为最优性判别函数。最后证明了算法的全局收敛性并分析了迭代复杂度。

A level bundle method based on Bregman distance for solving nonsmooth constrained convex optimization is proposed.The traditonal Euclidean distance is extended to the generalized Bregman distance,which can make use of the geometry of the feasible set.The proposed method utilizes polyhedral models to approximate the objective and constraint functions of the original problem,and introduces an improvement function as a certificate of optimality.Finally,the global convergence of the algorithm is proved and the iteration complexity is analyzed.