SQA: a generic trust region derivative free optimization method for black box industrial applications
Abstract
Derivative free optimization takes place in various application fields and often requires dedicated techniques to limit the number of evaluations of the usually time consuming simulator. We propose the Sequential Quadratic Approximation method (SQA) based on a trust region method with quadratic interpolation models. This method based on NEWUOA algorithm (Powell, 2004) is extended to constrained problems (derivative based and derivative free constraints) and to least-square and multi-objective formulations. A parallel version of this algorithm is studied to accelerate the convergence (in terms of CPU time) to a local minimum by using adapted model improvement steps and multi-model approach (incomplete quadratic models based on varying number of interpolation points). We show applications of SQA on classical DFO test problems and to an industrial application in reservoir characterization.