【摘要】 对求解无约束规划的共轭梯度算法中共轭梯度方向中的参数给了一个假设条件,从而确定它的一个取值范围,使其在此范围内取值均能保证共轭梯度方向是目标函数的充分下降方向,提出了一类新的共轭梯度算法,在去掉迭代点列有界和广义Armijo步长搜索下讨论了算法的全局收敛性。同时给出了具有好的收敛性质和较快收敛速度的FR,PR,HS共轭梯度法的修正形式。数值例子表明新算法比Armijo搜索下的FR,PR,HS共轭梯算法更稳定更有效。算法需要较小的存储,特别适于求解大规模无约束最优化问题。更多还原

【Abstract】 Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameter in the conjugate gradient directions. In this note, conditions are given on the parameter to ensure that the conjugate gradient direction is sufficient descent, and a new conjugate gradient method is presented. The convergence property of th new conjugate gradient method with generalized Armijo step size rule is discussed without assuming that the sequence of iterates is bounded. Combining FR, PR, HS methods with our new method, FR, PR, HS methods are modified to have global convergence property. Numerical result show that the new algorithm is efficient by comparing with FR, PR, HS conjugate gradient methods with Armijo step size rule.更多还原