Research Reports from the Department of Operations
Document Type
Report
Publication Date
7-10-1978
Abstract
The purpose of this research is to establish a computationally efficient algorithm for solving certain systems of convex equations. In the past, two basic approaches have been developed. The first approach is based on variations of Newton's method and requires rather stringent conditions on the system of equations whereas the second approach is based on the homotopic or continuation method which requires milder conditions for convergence. The approach in this work will be from an optimization standpoint and convergence will be established under reasonable conditions. In addition, a global algorithm for finding the zero of a convex real valued function of one variable will be developed with the property that if it terminates finitely then either it has computed a zero or determined that none exists. Furthermore, if an infinite sequence is generated, it either converges to a zero or again no such point exists. Algorithmic performance and applications will also be presented.
Keywords
Operations research, Algorithms, Convex functions, Mathematical optimization, Numerical analysis
Publication Title
Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 454
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Solow, Daniel, "A Constrained Optimization Algorithm for Solving Certain Convex Systems of Equations" (1978). Research Reports from the Department of Operations. 97.
https://commons.case.edu/wsom-ops-reports/97