非线性优化的广义投影变尺度算法及超线性收敛性

摘要

The authors presented a generalized project metric algorithm with arbitrary initial point for the optimized problem with nonlinear equality and inequality constraints with the aid of the idea of penalty function technique. In order to avoid Maratos effect, a high-order revised direction was generated by an explicit formula and its global convergence and superlinear convergence were obtained under some suitable assumptions. The numerical results show that the method in this paper is effective.%结合罚函数法的思想,提出一种初始点任意的广义投影变尺度算法求解非线性等式和不等式约束优化问题,克服了Maratos效应的校正方向自动产生显式表达式,并在适当的条件下证明了算法是全局收敛的,且具有超线性收敛性.实验结果表明算法有效.