Rapidly Convergent Algorithms for Nonsmooth Optimization.
Abstract
This research has led to new developments for solving nonlinear optimization problems involving functions that are not everywhere differentiable and/or are implicity defined. For the single variable case a method has been given which combined polyhedral and quadratic approximation, and automatic scale-free penalty technique and a safeguard that insures convergence to a stationary point, but does not detract from rapid convergence. Under relatively weak convergence rate assumptions the algorithm exhibits a new type of better than linear convergence. The safequard also has the practical advantage of keeping apart points that are used in denominators of difference quotients for approximating second derivatives. A practical single resource allocation problem with several bounded decision variables has been solved very efficiently via a dual technique that used the single variable method in a nested manner to solve both the outer dual problem and the inner Lagrangian subproblems. The new concept of better than linear convergence form the single variable case has been generalized to the multivariable case. Author supplied key words also include; constrained minimization, and line search.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 14, 1984
- Accession Number
- ADA145556
Entities
People
- R. Mifflin
Organizations
- Washington State University