Two Algorithms for Solving Unconstrained Global Optimization by Auxiliary Function Method

In this paper, we present two algorithms that are designed to solve unconstrained global optimization problems. The first algorithm is introduced for resolving unconstrained optimization problems by dividing a multidimensional problem into partitions of a one-dimensional problem and subsequently identifying a global minimizer for each partition by utilizing an auxiliary function and then using it to find the global minimizer of a multidimensional problem. In the second algorithm, the same auxiliary function is used to find a global minimizer of the same multidimensional problem without partitioning it. Finally, we apply these algorithms to common test problems and compare them to each other to show the efficiency of the algorithms