一类非单调三参数共轭梯度算法研究

虽然求解无约束优化问题共轭梯度方法的算法程序便于计算机上实现,但难于建立算法的全局收敛性理论.为弥补其不足,研究了一类新的共轭梯度算法.该算法搜索方向的构造中引入了3个参数,且通过合适地选取这些参数保证了所得搜索方向不依赖于线搜索技术,是目标函数的恒充分下降方向.以此为基础,提出了一种求解无约束优化问题的非单调三参数共轭梯度法,并在一定的假设条件下建立了算法的全局收敛性理论.数值实验进一步验证了这种算法比同类算法更有效.

Investigation on Nonmonotone Conjugate Gradient Algorithm with Three Parameters

Though conjugate gradient methods are easy to be implemented in a computer for solving an unconstrained optimization problem, it is difficult to establish the theory of global convergence. To overcome this difficulty,a new conjugate gradient algorithm was investigated. In this algorithm, the search direction is constructed to be involved with three parameters, which are suitably chosen such that the obtained direction is always sufficiently descent one of the objective function, independent of any line search strategy. On basis of this direction, a nonmonotone conjugate gradient algorithm with three parameters is developed for solving unconstrained optimization problems. Under some mild assumptions, the global convergence theorem of this algorithm is proved. Preliminary numerical experiments demonstrate that the developed algorithm is more effective than the similar algorithms.