In this survey article we give the basic description of the interpolation based derivative free optimization methods and their variants. We review the recent contributions dealing with the maintaining the geometry of the interpolation set, the management of the trust region radius and the stopping criteria. Derivative free algorithms developed for problems with some structure like for partially separable functions are discussed. Two different versions of derivative free algorithms are applied for the optimization of the configuration of the geometry of a stirrer. Numerical results are presented to show the applicability of the algorithms to practical problems.
published in Journal of Industrial and Management Optimization, Volume: 3, Number: 2, May 2007, pp. 321-334