固定步长修正LS共轭梯度法的全局收敛性

Global Convergence Properties of the Modified LS Conjugate Gradient Method with Fixed Step-size

基于修正LS共轭梯度法,给出步长公式,使无线搜索算法的迭代过程自动满足充分下降性.在水平集中目标函数有界和梯度函数Lipschitz连续的条件下,分别证明了采用固定步长和常数步长的算法具有全局收敛性.

Base on the modified LS conjugate method, the step-size formula for the algorithm without line search is proposed, which make the sufficient descent property holds at each iteration. Under the bound- edness of the objective function on the level set and the Lipschitz continuity of the gradient function, global convergence of the corresponding algorithms with fixed step-size and constant step--size are proved, respectively.