一类Armijo搜索下的混合HS-PRP共轭梯度法

Hybrid HS-PRP Conjugate Gradient Method with Armijo Line Search

为有效求解大规模无约束优化问题,本文基于HS方法和PRP方法,提出了一类新的混合共轭梯度法.该方法在每步迭代中都不依赖于函数的凸性和搜索条件而自行产生充分下降方向.在精确搜索下,本文算法将还原为标准的PRP方法.在适当的条件下,获证了该法在Armijo搜索下,即使求解非凸函数极小化的问题,算法也具有全局收敛性.同时,数值实验表明本文算法可以有效求解优化测试问题.

Based on the HS method and the PRP method, a new kind of hybrid conjugate gradient methods for solving large scale unconstrained optimization problems is proposed. The modified method provides automatically a sufficient descent direction for the objective function at each iteration, a property depends neither on the line search used, nor on the convexity of the function. If the exact line search is used, the given method reduces to the standard PRP method. Under mild conditions, the proposed method with the Armijo line search converges globally even if the objective function is nonconvex. Numerical results show that the new method is efficient and can be used to deal with some test problems.