非光滑约束优化带束集修正的两阶段束方法

A Two-phase Bundle Method with Bundle Modification for Nonsmooth Constrained Optimization

结合两阶段束方法思想,提出新的束集修正策略,得到一个求解非光滑约束优化问题的两阶段束方法.当稳定中心更新时,通过束集修正策略,约束函数值更小的新点将替代束集中的一部分不可行点,目标函数值更小的新点将替代一部分可行点,旨在得到质量更优的束集.算法能接受不可行初始点,在阶段一搜索一个可行迭代点,一旦产生可行迭代点,进入阶段二执行可行方向算法.算法具备全局收敛性,且初步的数值结果表明算法是有效的.

In this paper,a new bundle modification strategy is proposed based on the idea of two-phase bundle method,and then a two-phase bundle method for nonsmooth constrained optimization problem is presented.When the stability center is updated,by applying the bundle strategy,some unfeasible points in the bundle will be substituted by new ones which have lower constraint values,and some feasible points will be substituted by new ones which have lower objective values,aiming at getting a better bundle.The method can accept infeasible initial points.When a feasible iterate is generated in phase I,the method will proceed as a feasible direction algorithm in phase II.The method possesses global convergence and preliminary computational results show that the algorithm is effective.