A generalized Dai-Liao type CG-method with a new monotone line search for unconstrained optimization

Abstract

In this paper, we presented two developments, the first deals with generalizing the modernization of the damped Dai-Liao formula in an optimized manner. The second development is by suggesting a monotone line search formula for our new algorithms. These new algorithms with the new monotone line search yielded good numerical results when compared to the standard Dai-Liao (DL) and minimum description length (MDL) algorithms. Through several theorems, the new algorithms proved to have a faster convergence to reach the optimum point. These comparisons are drawn in the results section for the tools (Iter, Eval-F, Time) which are a comprehensive measure of the efficiency of the new algorithms with the basic algorithms that we used in the paper.