Research Reports from the Department of Operations
Document Type
Report
Publication Date
1-1-1964
Abstract
In this part certain conditions are established under which an equilibrium point of the algorithm of price-adjustment (P - E) is asymptotically stable in the large. These conditions are phrased as requirements on the functions involved in the original or integrated problem. It is shown that although the usual concavity requirements (for maximization problems) are sufficient to guarantee stability, much less will suffice. Mathematically, this appears as the fact that, for stability, only the sum of certain quadratic forms - one for each sub-problem - must be negative, so that one or more positive terms may be cancelled by others sufficiently negative. An "organizational" interpretation of this result is attempted.
Keywords
Operations research, Mathematical optimization, Control theory, Decentralization in management, Equilibrium (Economics), Resource allocation. System analysis, Computational complexity, Concave functions
Publication Title
Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 13
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Lasdon, Leon S. and Sengupta, S. Sankar, "Decentralized Management of Interacting Processes: A Technique of Nonlinear Programming (II)" (1964). Research Reports from the Department of Operations. 123.
https://commons.case.edu/wsom-ops-reports/123