A class of derivative-free nonmonotone optimization algorithms employing coordinate rotations and gradient approximations

In this paper we study a class of derivative-free unconstrained minimization algorithms employing nonmonotone inexact linesearch techniques along a set of suitable search directions. In particular, we define globally convergent nonmonotone versions of some well-known derivative-free methods and we propose a new linesearch-based nonmonotone algorithm, where search directions are constructed by combining coordinate rotations with simplex gradients. Through extensive numerical experimentation, we show that the proposed algorithm is highly competitive in comparison with some of the most efficient direct search methods and model based methods on a large set of test problems. Copyright Springer Science+Business Media New York 2015