论文标题
部分可观测时空混沌系统的无模型预测
A Modified Nonlinear Conjugate Gradient Algorithm for Functions with Non-Lipschitz Gradient
论文作者
论文摘要
在本文中，我们提出了一种改进的非线性结合梯度（NCG）方法，用于具有非lipschitz连续梯度的功能。首先，我们为NCG中的结合系数β_K提出了一个新公式，从而进行了一个搜索方向，该方向提供了足够的功能降低。我们可以得出我们的NCG算法可以保证在没有Lipschitz连续梯度的情况下，对连续差异功能有强烈的收敛。其次，我们提出了一种简单的插值方法，该方法可以自动实现收缩，从而产生一个满足每个步骤中标准狼条件的步长。我们的框架大大扩展了NCG的适用性，并保留了PRP型方法的出色数值性能。
In this paper, we propose a modified nonlinear conjugate gradient (NCG) method for functions with a non-Lipschitz continuous gradient. First, we present a new formula for the conjugate coefficient β_k in NCG, conducting a search direction that provides an adequate function decrease. We can derive that our NCG algorithm guarantees strongly convergent for continuous differential functions without Lipschitz continuous gradient. Second, we present a simple interpolation approach that could automatically achieve shrinkage, generating a step length satisfying the standard Wolfe conditions in each step. Our framework considerably broadens the applicability of NCG and preserves the superior numerical performance of the PRP-type methods.
