SQPDFO – A trust-region based algorithm for generally-constrained derivative-free optimization

Derivative-free optimization is a specific branch of mathematical where first and higher order derivatives the objective function problem are not available, too expensive to compute or inexact be used. Such problems do arise in many application areas, e.g., engineering design optimization, wastewater treatment quantum chemical processes. As only value information no derivative SQPDFO applies different sampling techniques build local interpolation models constraint functions uses self-correcting error technique (Scheinberg Toint [1]) which guarantees quality these their during process. Throughout process, second can handle nonlinear linear equality inequality constraints simple bounds on variables. It based SQP (Sequential Quadratic Programming) method solves sequence subproblems, each optimizes quadratic program original problem. Inequality carefully handled by slack variables included unnecessarily increase size matrix. We will present numerical results large set academic test from well-known library CUTEst showing good performance implementation SQPDFO. Furthermore, we extended code run parallel several evaluations used iteration. This was especially useful when applying multidisciplinary DLR research shape an entire airplane. one complete evaluation top-level take up 56 hours, needs minimum number iterations crucial. show how able find solutions within very small iterations.