We consider the problem of minimizing a continuously differentiable function of several variables subject to simple bound and general nonlinear inequality constraints, where some of the variables are restricted to take integer values. We assume that the first order derivatives of the objective and constraint functions can be neither calculated nor approximated explicitly. This class of mixed integer nonlinear optimization problems arises frequently in many industrial and scientific applications and this motivates the increasing interestin the study ofderivative-freemethods fortheir solution. The continuous variables are handled by a linesearch strategy whereas to tackle the discrete ones we employ a local search-type approach. Nonlinear constraints are handled by using a quadratic penalty function approach. We propose two algorithms which are characterized by the way the current iterate is updated and by the stationarity conditions satisfied by the limit points of the sequences they produce. We report a computational experience both on standard test problems and on a real optimal design problem. We also compare the performances of the proposed methods with those of a well-known derivative-free optimization software package, i.e. NOMAD
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