Second Order Behavior of Pattern Search
Abstract
Abstract. Previous 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2004
- Accession Number
- ADA453255
Entities
People
- Mark A. Abramson
Organizations
- Air Force Institute of Technology