Computational Algorithm for Unconstrained Minimization.
Abstract
A generalized descent algorithm theory is developed for unconstrained minimization problems. Here a descent algorithm is defined as a computational procedure where at each iteration a descent direction is determined and a single dimensional search is made for the minimum in the descent direction. The theory is shown to be a generalization of the three most common descent algorithms; gradient, conjugate gradient and Fletcher-Powell. Since execution of the single dimensional search can be computationally time consuming, two additional algorithms are presented which reduce or eliminate single dimensional search time. The first is a modification of Davidon's Variance Algorithm and requires a minimal single dimensional search. The second is a direct method for minimizing a special class of quadratic functions. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1972
- Accession Number
- AD0747277
Entities
People
- Bruce T. Kujawski
Organizations
- Air Force Institute of Technology