Abramson, Mark A.2018-06-182018-06-182004-01Abramson, Mark A.. "Second Order Behavior of Pattern Search Algorithms." (2004) <a href="https://hdl.handle.net/1911/102016">https://hdl.handle.net/1911/102016</a>.https://hdl.handle.net/1911/102016Previous analyses of pattern search algorithms for unconstrained and linearly constrained minimization have focused on proving convergence of a subsequence of iterates to a limit point satisfying either directional or first-order necessary conditions for optimality, depending on the smoothness of the objective function in a neighborhood of the limit point. Even though pattern search methods require no derivative information, we are able to prove some limited directional second-order results. Although not as strong as classical second-order necessary conditions, these results are stronger than the first order conditions that many gradient-based methods satisfy. Under fairly mild conditions, we can eliminate from consideration all strict local maximizers and an entire class of saddle points.16 ppengTechnical reportTR04-03