An Improved Spectral Conjugate Gradient Algorithm Based on A Modified Wolfe Line Search

TL;DR

This paper introduces an enhanced spectral conjugate gradient algorithm that integrates a modified Wolfe line search and higher-accuracy secant equations, improving convergence for nonconvex optimization problems.

Contribution

It develops a novel spectral conjugate gradient method with modified secant equations and Wolfe line search, ensuring global convergence for nonconvex functions.

Findings

Algorithm demonstrates improved convergence behavior.

Numerical tests verify effectiveness and robustness.

Outperforms existing methods on benchmark problems.

Abstract

In this paper, we combine the $m$th-order Taylor expansion of the objective function with cubic Hermite interpolation conditions. Then, we derive a series of modified secant equations with higher accuracy in approximation of the Hessian matrix of the objective function. A modified Wolfe line search is also developed. It overcomes the weakness of the typical constraint which is imposed on modified secant equations and to keep the curvature condition met. Therefore, based on the modified secant equation and Wolfe line search, an improved spectral conjugate gradient algorithm is proposed. Under some mild assumptions, the algorithm is showed to be globally convergent for general nonconvex functions. Numerical results are also reported for verifying the effectiveness.