Numerical experience with a derivative-free trust-funnel method for nonlinear optimization problems with general nonlinear constraints

A trust-funnel method is proposed for solving nonlinear optimization problems with general nonlinear constraints. It extends the one presented by Gould and Toint (Math. Prog., 122(1):155- 196, 2010), originally proposed for equality-constrained optimization problems only, to problems with both equality and inequality constraints and where simple bounds are also considered. As the original one, our method makes use of neither filter nor penalty functions and considers the objective function and the constraints as independently as possible. To handle the bounds, an active set approach is employed. We then exploit techniques developed for derivative-free optimization to obtain a method that can also be used to solve problems where the derivatives are unavailable or are available at a prohibitive cost. The resulting approach extends the DEFT-FUNNEL algorithm presented by Sampaio and Toint (Comput. Optim. Appl., 61(1):25-49, 2015), which implements a derivative-free trust-funnel method for equality-constrained problems. Numerical experiments with
the extended algorithm show that our approach compares favorably to other well-known mode-lbased algorithms for derivative-free optimization.