Two types of interpretations of multipliers in both static and dynamic optimization problems are described. It is snown that the Lagrange multipliers encountered in mathematical programming problems and the auxiliary functions arising in Pontryagintype optimal control problems sometimes have highly analogous interpretations as rates of change of the optimal attainable value of an objective function, or in some cases as bounds on average rates of change.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Wilde, D. J., andBeightler, C. S.,Foundations of Optimization, Prentice-Hall, Englewood Cliffs, New Jersey, 1967.
Zangwill, W. I.,Nonlinear Programming: A Unified Approach, Prentice-Hall, Englewood Cliffs, New Jersey, 1969.
Luenberger, D. G.,Optimization by Vector Space Methods, John Wiley and Sons, New York, New York, 1969.
Dorfman, R.,An Economic Interpretation of Optimal Control Theory, American Economic Review, Vol. 59, pp. 817–831, 1969.
Lee, E. B., andMarkus, L.,Foundations of Optimal Control Theory, John Wiley and Sons, New York, New York, 1968.
Hestenes, M. R.,Calculus of Variations and Optimal Control Theory, John Wiley and Sons, New York, New York, 1966.
Courtin, P., andRootenberg, J.,Performance Index Sensitivity of Optimal Control Systems, IEEE Transactions on Optimal Control, Vol. 16, pp. 275–277, 1971.
Intriligator, M. D.,Mathematical Optimization and Economic Theory, Prentice-Hall, Englewood Cliffs, New Jersey, 1971.
Peterson, D. W.,The Economic Significance of Auxiliary Functions in Optimal Control, International Economic Review, Vol. 14, pp. 234–252, 1973.
Communicated by M. R. Hestenes
About this article
Cite this article
Peterson, D.W. On sensitivity in optimal control problems. J Optim Theory Appl 13, 56–73 (1974). https://doi.org/10.1007/BF00935609
- Sensitivity analysis
- control theory
- mathematical programming
- method of multipliers
- Banach spaces