A Benchmark Study on Steepest Descent and Conjugate Gradient Methods-Line Search Conditions Combinations in Unconstrained Optimization

In this paper, it is aimed to computationally conduct a performance benchmarking for the steepest descent and three well-known conjugate gradient methods (i.e., Fletcher-Reeves, Polak-Ribiere Hestenes-Stiefel) along with six different step length calculation techniques/conditions, namely Backtracking, Armijo-Backtracking, Goldstein, weakWolfe, strongWolfe, Exact local minimizer in unconstrained optimization. To end, series of computational experiments on test function set completed using combinations those optimization line search conditions. During these experiments, number evaluations every iteration are monitored recorded all method-line condition combinations. The total then measure when combination question converges functions minimums within given convergence tolerance. Through data, data profiles created purpose reliable an efficient benchmarking. It has been determined that, set, descent-Goldstein fastest one whereas descent-exact most robust high accuracy. By making trade-off between speed robustness, identified that descent-weak Wolfe optimal choice set.