Pattern Search Methods for Linearly Constrained Minimization

We extend pattern search methods to linearly constrained minimization. We develop a general class of feasible point pattern search algorithms and prove global convergence to a Karush--Kuhn--Tucker point. As in the case of unconstrained minimization, pattern search methods for linearly constrained problems accomplish this without explicit recourse to the gradient or the directional derivative of the objective. Key to the analysis of the algorithms is the way in which the local search patterns conform to the geometry of the boundary of the feasible region.