A Derivative-Free Algorithm for Constrained Global Optimization Based on Exact Penalty Functions

Constrained global optimization problems can be tackled by using exact penalty approaches. In a preceding paper, we proposed an exact penalty algorithm for constrained problems which combines an unconstrained global minimization tech- nique for minimizing a non-differentiable exact penalty function for given values of the penalty parameter, and an automatic updating of the penalty parameter that oc- curs only a finite number of times. However, in the updating of the penalty parameter, the method requires the evaluation of the derivatives of the problem functions. In this work, we show that an efficient updating can be implemented also without using the problem derivatives, in this way making the approach suitable for globally solving constrained problems where the derivatives are not available. In the algorithm, any efficient derivative-free unconstrained global minimization technique can be used. In particular, we adopt an improved version of the DIRECT algorithm. In addition, to impr