Article ID: | iaor20134160 |
Volume: | 56 |
Issue: | 3 |
Start Page Number: | 1217 |
End Page Number: | 1232 |
Publication Date: | Jul 2013 |
Journal: | Journal of Global Optimization |
Authors: | Martnez J, Sobral F |
Keywords: | iterative methods, penalty functions |
Many derivative‐free methods for constrained problems are not efficient for minimizing functions on ‘thin’ domains. Other algorithms, like those based on Augmented Lagrangians, deal with thin constraints using penalty‐like strategies. When the constraints are computationally inexpensive but highly nonlinear, these methods spend many potentially expensive objective function evaluations motivated by the difficulties in improving feasibility. An algorithm that handles this case efficiently is proposed in this paper. The main iteration is split into two steps: restoration and minimization. In the restoration step, the aim is to decrease infeasibility without evaluating the objective function. In the minimization step, the objective function