In this paper we define an iterative algorithm which uses only function values for finding an optimal solution to the problem min {$\varphi(x) | x \in X$}, where X is a convex polytope. It is shown that using this algorithm one can reduce the initial problem to a finite number of subproblems of the type min{$\varphi(x) | x \in C$}, where C is a linear manifold. It is also shown that each cluster point of the sequence generated by the algorithm presents an optimal point to the considered optimization problem.