Research Reports from the Department of Operations
Document Type
Report
Publication Date
8-1-1969
Abstract
It is now well known that the most efficient methods for unconstrained minimization which do not require second derivatives are those which, when applied to a quadratic, generate conjugate directions [1-4]. This insures that a quadratic in n variables is minimized in n steps or less. Since a general twice differentiable function behaves like a positive semidefinite quadratic in the neighborhood of its minimum, methods which will minimize it efficiently must work well on a quadratic. Conjugate direction methods meet this requirement, do not require second derivatives, and can be constructed so that the function is reduced at each step. Here we review the principles upon which these methods are based. Then some specific algorithms are derived. These have been presented in references [1] and [7]; the derivations here are included for clarity and completeness. Finally, the use of these algorithms in infinite dimensional spaces is considered.
Keywords
Operations research, Mathematical optimization, Conjugate gradient methods, Quadratic programming, Algorithms, Numerical analysis, Calculus of variations, Functional analysis
Publication Title
Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 157
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Lasdon, Leon S., "Efficient Methods for Unconstrained Minimization" (1969). Research Reports from the Department of Operations. 179.
https://commons.case.edu/wsom-ops-reports/179