非单调线搜索下的记忆梯度法及其全局收敛性

A Memory Gradient Method with Nonmonotone Line Search and Its Global Convergence

提出一种新的非单调线搜索准则,结合文献中给出的dk,研究一类新的记忆梯度法,在较弱条件下证明了其全局收敛性.算法采用新的非单调线搜索准则,使目标函数值在每一次迭代时充分下降,有效降低了算法的计算量,同时还减弱了文献中算法的使用条件,从而扩大了算法求解问题的范围.

This paper develops a new nonmonotone line search and investigates a new class of memory gradient methods based on the dk which presented.The globle convergence of the method is proved under some mild conditions.By using the new nonmonotone line search,the method sufficiently reduces the function evaluations at each iteration and efficiently decreases the computation.Moreover,the method weakens the using conditions of algorithm so as to extend its range of solving the problems.