A projection method for linearly constrained problems which only uses function values

This paper defines an iterative algorithm which uses only function values for finding an optimal solution to the problem min{ℝrsquo;(x)•x∈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{ℝrsquo;(x)•x∈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.