A discrete projection quasi-Newton method for linearly constrained problems

This paper defines a discrete quasi-Newton 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 is an optimal point of the considered optimization problem.