This paper shows the equivalence of entropy-maximization models to geometric programs. As a result we derive a dual geometric program which consists of the minimization of an unconstrained convex function. We develop the necessary duality equivalencies between the two dual programs and show the computational attractiveness of our approach. We also develop some characterizations of the optimal solution of the entropy model which have important implications with regard to postoptimal or sensitivity analysis.
Get full access to this article
View all access options for this article.
References
1.
ChampernowneAWilliamsH CCoelhoJ, 1976“Some comments on urban travel demand analysis, model calibration and the economic evaluation of transport models”Journal of Transport Economics and Policy September 1976, pp 267–285.
2.
CharnesACooperW W, 1974“An external principle for accounting balance of a resource value-transfer economy”Rendiconti di Academia Nazionale dei Lincei56 (4) 556–561.
3.
CharnesAHaynesK EPhillipsF Y, 1974“A generalized distance estimation procedure for intraurban interaction” RR CCS171, Center for Cybernetic Studies, University of Texas, Austin, Tex.
4.
CharnesAHaynesK EPhillipsF YWhiteG, (forthcoming) “New equivalencies and dualities from the extremal solution of the gravity model of spatial interaction: An approach using the unconstrained dual of an extended geometric programming problem”Journal of Regional Science.
5.
CharnesARaikeW MBettingerC O, 1972“An extremal and information-theoretic characterization of some interzonal transfer models”Socio-Economic Planning Science6531–537.
6.
CoelhoJ DWilsonA G, 1977“Some equivalence theorems to integrate entropy maximization submodels within overall mathematical programming frameworks”Geographical Analysis (forthcoming).
7.
DinkelJ JKochenbergerG A, 1977“Sensitivity analysis in geometric programming”Operations Research25155–163.
8.
DinkelJ JKochenbergerG AWongS-N, 1977“Sensitivity analysis of regional planning models”Environment and Planning A985–98.
9.
DuffinR JPetersonE LZenerC, 1967Geometric Programming (John Wiley, New York).
10.
EvansS P, 1976“Derivation and analysis of some models for combining trip distribution and assignment”Transportation Research1037–57.
11.
JeffersonTScottC, 1975“Entropy and geometric programming in transportation planning” submitted toTransportation Science.
12.
NijkampPPaelinckJ, 1974“A dual interpretation and generalization of entropy-maximization models in regional science”Papers of the Regional Science Association3313–31.
13.
PhillipsFWhiteG M, 1974“Extremal approaches to estimating spatial interaction” RR CCS168, Center for Cybernetic Studies, University of Texas, Austin, Tex.
14.
ScottA J, 1974“A theoretical model of pedestrian flow”Socio-Economic Planning Science8317–322.
15.
WilsonA G, 1970Entropy in Urban and Regional Modelling (Pion, London).
16.
WilsonA GSeniorM L, 1974“Some relationships between entropy maximizing models, mathematical programming models, and their duals”Journal of Regional Science14207–215.
