Delaunay-based optimization is a generalizable family of practical, efficient, and provably convergent derivative-free algorithms designed for a range of black-box optimization problems with expensive function evaluations. In many practical problems, the calculation of the true objective function is not exact for any feasible set of the parameters. For problems of this type, a variant of Delaunay-based optimization algorithms dubbed α -DOGS is designed to efficiently minimize the true objective function evaluated with sampling error, while using minimal sampling over the parameter space. In the present work, we extend α-DOGS to additionally address uncertainties of the objective function that are generated by the numerical discretization of the ODE or PDE problems of interest. For validation, this modified optimization algorithm is applied to the (chaotic) Lorenz system. Numerical results indicate that, following the new approach, most of the computational effort is spent close to the optimal solution as convergence is approached.
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