线性不等式约束优化的弧线路径信赖域算法

提供了弧线路径结合仿射内点信赖域策略的非单调回代算法解线性不等式约束的优化问题.基于仿射投影的信赖域子问题获得新的搜索方向,采用弧线路径的近似信赖域和线搜索结合技术得到回代步,获得新的步长.通过证明所提供的弧线路径具有一系列良好性质,从而在合理的条件下,证明所提供的算法不仅具有整体收敛性,而且保持算法的局部超线性收敛速率.数值测试表明了算法的有效性与可靠性.

Nonmonotonic backtracking trust region strategy algorithm via curvilinear path for nonlinear optimizations subject to linear inequality constraints

The paper modifies a type approximate trust region method via the curvilinear path for nonlinear optimizations subject to linear inequality constraints. A mixed strategy using both interior trust region arid line search technique is adopted which switches to backtracking steps when a trial step produced by the affine scaling trust region subproblem is unacceptable. The global convergence and fast local convergence rate of the proposed algorighm are established under some reasonable conditions. A nonmonotonic criterion is used to speed up the convergence progress in some ill-conditioned cases. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.