<p>In this study, we present an adaptive restarting RMIL conjugate gradient (CG) method and its hybrid version for solving unconstrained optimization problems. First, we introduce an effective restarting direction and integrate it into the RMIL CG method. The resulting composite search direction, independent of any line search, possesses the sufficient descent property. Then, by using the hybrid strategy presented in [Applied Mathematical Modelling 39 (2015) 1281–1290], we obtain a hybrid RMIL CG method with a restarting mechanism, whose search direction also has the desired properties. Furthermore, we demonstrate the global convergence of the two proposed methods under conventional assumptions, where the step sizes are determined using the weak Wolfe line search. Additionally, by using the Armijo line search to determine step sizes, we derive the iterative complexity of the obtained methods. Numerical experiments comparing our methods with existing methods confirm their efficiency in addressing unconstrained optimization problems. Finally, we employ the proposed methods for image restoration tasks.</p>