Nonlinear Optimization Using Adaptive Restarting Conjugate Gradient Methods

Conjugate gradient methods are optimization techniques used to minimize cost functions in nonconvex problem domains. However, in non-quadratic conjugate gradient methods, challenges often arise due to exact line searches and the need for effective restart procedures to enhance convergence properties. This paper introduces a modified conjugate gradient method that incorporates adaptive restarting, specifically designed for nonconvex objective functions, with the goal of preventing stagnation in convergence iterations. The adaptive restarting conjugate gradient approach aims to increase the likelihood of eliminating convergence stagnation. Through numerical investigations, the paper demonstrates the superior performance of the proposed restarting method, showcasing improved convergence behavior by effectively mitigating stagnation in the convergence process.