关键词: 无约束最优化;共轭梯度法;Armijo型线搜索;全局收敛性

Abstract:

A new nonlinear modified spectral CD conjugate gradient method is dealt with. The direction generated by the method is a descent direction for the objective function, and this property depends neither on the line search used, nor on the convexity of the objective function. Moreover, the modified method reduces to the standard CD method if line search is exact. It proves that the modified method with Armijo-type line search I or II is globally convergent. Preliminary numerical results show the proposed method is very promising.

Key words: unconstrained optimization; conjugate gradient method; Armijo-type line search;global convergence