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

          Ph. R. Sampaio and Ph. L. Toint          August 12, 2015
	  
Abstract
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 lter nor penalty functions and considers the
objective function and the constraints as independently as possible. To handle the bounds, an activeset
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 modelbased
algorithms for derivative-free optimization.