A Derivative-Free and Ready-to-Use NLP Solver for Matlab or Octave

This paper introduces a derivative-free and ready-to-use solver for nonlinear programs with nonlinear equality and inequality constraints (NLPs). Using finite differences and a sequential quadratic programming (SQP) approach, the algorithm aims at finding a local minimizer and no extra attempt is made to generate a globally optimal solution. Due to the use of finite differences, approximations of the derivatives are expensive compared to the numerical computations that usually dominate the computational effort of NLP solvers. This fact motivates the use of a somewhat effortful trust-region SQPsubproblem that is solved by second orde cone programs. The implementation in Matlab or Octave is easy to use and public domain; numerical experiments indicate that the algorithm is well suitable for problems with m inequality constraints depending on n variables when n+m ≤ 500.