A class of derivative free three-term descent Hestenes-Stiefel conjugate gradient algorithms for constrained nonlinear problems

Abstract

This paper presents a novel method for solving large-scale nonlinear monotone equations with convex constraints. The method builds upon the conjugate gradient approach and incorporates a search direction of three terms, complemented by a modified line search. The proposed method generates a search direction that guarantees sufficient descent property, irrespective of the line search technique used. We establish the global convergence of the method under mild conditions and conduct numerical experiments to compare it with existing algorithms from the literature. The results demonstrate the method’s effectiveness and robustness, highlighting its potential for practical applications.

Keywords

• Unconstrained optimization
• Nonlinear equations
• Monotone operator
• Conjugate gradient