一种改进的带非单调线搜索锥模型信赖域算法

An improved trust region algorithm with non-monotone Line search cone model

针对非单调锥模型信赖域算法求解子问题的接受条件中所存在的一些不合理因素,提出了一种新的改进的无约束优化算法.该算法在每一步都采用非单调Wolfe线搜索,求得下一个迭代点,并改变预计下降量,使其与实际下降量对应起来,这样做不仅不需要重解子问题,而且提高了梯度精度,一定的条件下证明了该算法的全局收敛性和Q-二次收敛性.

A new and improved unconstrained optimization algorithm is proposed for some unreasonable factors existed in the acceptable conditions of solving sub-problems of non-monotone cone model trust region algorithm.In each step,the non-monotonic Wolfe line is used to search for the next iteration point,and the estimated drop is changed to correspond to the actual drop.In this way,not only the resolver problem is not required,but also the gradient accuracy is improved.Under certain conditions,the global convergence and Q-quadratic convergence of the algorithm are proved.