非光滑单值优化的信赖域算法

摘要

提供了求解非光滑单值优化问题的信赖域算法.基于线性规划的对偶理论,将目标函数的方向导数转化成线性规划,从而使信赖域子问题容易数值求解.在合理的条件下,证明了算法的整体收敛性和局部超线性收敛速率.%Presents a trust region algorithm for nonsmooth unary optimization problems. Based on the duality theorem of linear programming, the directional derivatives of the objective function can be expressed as a linear programming which is very important in the practical calculution of trust region subproblems. Gives a theoretical analysis which proves that the proposed algorithm is globally convergent and has a local superlinear rate under some reasonable conditions.