Mathematics – Optimization and Control
Scientific paper
2011-06-05
Mathematics
Optimization and Control
Scientific paper
Verifying the Second-Order Sufficient Condition (SOSC), thus ensuring a stationary point locally minimizes a given objective function (subject to certain constraints), is an essential component of non-convex computational optimization and equilibrium programming. This article proposes three new "Hessian-free" tests of the SOSC that can be implemented efficiently with gradient evaluations alone and reveal feasible directions of negative curvature when the SOSC fails. The Bordered Hessian Test and a Matrix Inertia test, two classical tests of the SOSC, require explicit knowledge of the Hessian of the Lagrangian and do not reveal feasible directions of negative curvature should the SOSC fail. Computational comparisons of the new methods with classical tests demonstrate the relative efficiency of these new algorithms and the need for careful study of false negatives resulting from accumulation of round-off errors.
No associations
LandOfFree
Hessian-Free Methods for Checking the Second-Order Sufficient Conditions in Equality-Constrained Optimization and Equilibrium Problems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Hessian-Free Methods for Checking the Second-Order Sufficient Conditions in Equality-Constrained Optimization and Equilibrium Problems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hessian-Free Methods for Checking the Second-Order Sufficient Conditions in Equality-Constrained Optimization and Equilibrium Problems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-307855