Research Reports from the Department of Operations
Document Type
Report
Publication Date
7-1-1971
Abstract
One of the noble aims of dynamic programming at its conception -- namely, that of developing an operational method for the numerical solution of various control problems, is often thwarted for meaningfully scaled systems, by the curse of dimensionality. By far the most important contribution to modern dynamic programming is the development of efficient algorithms capable of being used, with present-day computational devices, to solve problems of a large-scale nature. Consequently, a number of algorithms have appeared in the literature in recent times, each geared towards ameliorating the above curse. The purpose of this paper is to present a didactic treatment and comparison of a set of three algorithms in two sample problems. An attempt is made to uncover some pitfalls in these algorithms and to dwell on situations where the use of these algorithms may pose a problem. The idea is to further optimum employment of the algorithms discussed in this paper.
Keywords
Operations research, Dynamic programming, Algorithms, Control theory--Mathematical models, Computational complexity, Numerical analysis--Data processing, Problem solving--Mathematical models, Mathematical optimization
Publication Title
Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 237
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Esogbue, Augustine O. and Singh, Amar J., "Reduction of Dimensionality in Dynamic Programming of Higher Dimensions: A Comparative Study and Analysis of Computational Aspects" (1971). Research Reports from the Department of Operations. 470.
https://commons.case.edu/wsom-ops-reports/470