A Pattern Search Filter Method for Nonlinear Programming without Derivatives

This paper formulates and analyzes a pattern search method for general constrained optimization based on filter methods for step acceptance. Roughly, a filter method accepts a step that either improves the objective function value or the value of some function that measures the constraint violation. The new algorithm does not compute or approximate any derivatives, penalty constants or Lagrange multipliers. A key feature of the new algorithm is that it preserves the useful division into global SEARCH and local POLL steps. It is shown here that the algorithm identifies limit points at which optimality conditions depend on local smoothness of the functions. Stronger optimality conditions are guaranteed for smoother functions. In the absence of general constraints, the proposed algorithm and its convergence analysis generalize the previous work on unconstrained, bound constrained and linearly constrained generalized pattern search. The algorithm is illustrated on some test examples and on an industrial wing planform engineering design application.