Mathematics

CLC number: O221.2

A New Two-Parameter Family of Nonlinear Conjugate Gradient Method Without Line Search for Unconstrained Optimization Problem

无约束优化问题的一种新的无线搜索的两参数族非线性共轭梯度法

School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, Inner Mongolia Autonomous Region, China

Received: 28 November 2023

Abstract

This paper puts forward a two-parameter family of nonlinear conjugate gradient (CG) method without line search for solving unconstrained optimization problem. The main feature of this method is that it does not rely on any line search and only requires a simple step size formula to always generate a sufficient descent direction. Under certain assumptions, the proposed method is proved to possess global convergence. Finally, our method is compared with other potential methods. A large number of numerical experiments show that our method is more competitive and effective.

摘要

针对无约束优化问题，提出了一种无需线搜索的两参数族非线性共轭梯度法。该方法的主要特点是不依赖于任何线搜索，仅需要一个简单的步长公式总能产生充分下降的方向。在一定的假设条件下，证明了该方法具有全局收敛性。最后，我们的方法与其他数值效果较好的方法进行了比较。大量的数值实验表明，该方法更具有竞争力和有效性。