In this paper, we take advantage of the availability of higher-order derivatives through the table method (see Ref. 1) and suggest a simple variant of the Lagrangian method for constrained optimization. Our method, and the software that we currently have can be used to minimize functions with many variables subject to an arbitrary number of constraints.
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.
Kalaba, R., andTishler, A.,Optimization in Nonlinear Models via Automatic Derivative Evaluation, University of Southern California, Department of Economics, Working Paper No. 8214, 1982.
Kalaba, R., Tesfatsion, L., andWang, J. L.,A Finite Algorithm for the Exact Evaluation of Higher-Order Partial Derivatives of Functions of Many Variables, Journal of Mathematical Analysis and Applications (to appear).
Kalaba, R., andTishler, A.,A Generalized Newton Algorithm Using Higher-Order Derivatives, Journal of Optimization Theory and Applications, Vol. 39, pp. 1–17, 1983.
Kalaba, R., andTishler, A.,A Computer Program for Optimization of Functions with Many Variables Using Computer-Evaluated Exact Higher-Order Derivatives, Applied Mathematics and Computation, Vol. 13, pp. 143–172, 1983.
Miele, A., andLevy, A. V.,Modified Quasilinearization and Optimal Initial Choice of the Multipliers, Part 1, Mathematical Programming Problems, Journal of Optimization Theory and Applications, Vol. 6, pp. 364–380, 1970.
Miele, A., Iver, R. R., andWell, K. H.,Modified Quasilinearization and Optimal Initial Choice of the Multipliers, Part 2, Optimal Control Problems, Journal of Optimization Theory and Applications, Vol. 6, pp. 381–409, 1970.
Kalaba, R., andTishler, A.,A Generalized Newton Algorithm to Minimize a Function with Many Variables Using Computer-Evaluated Exact Higher-Order Derivatives, Journal of Optimization Theory and Applications (to appear).
Lootsma, F. A.,A Survey of Methods for Solving Constrained Minimization Problems via Unconstrained Minimization, Numerical Methods for Nonlinear Optimization, Edited by F. A. Lootsma, Academic Press, New York, New York, 1972.
Avriel, M.,Nonlinear Programming: Analysis and Methods, Prentice-Hall, Englewood Cliffs, New Jersey, 1976.
Henderson, J. M., andQuandt, R. E.,Microeconomic Theory, McGraw-Hill, New York, New York, 1980.
On leave from the Faculty of Management, Tel Aviv University, Tel Aviv, Israel.
About this article
Cite this article
Kalaba, R., Tishler, A. On the use of the table method in constrained optimization. J Optim Theory Appl 43, 157–165 (1984). https://doi.org/10.1007/BF00936161
- Constrained optimization
- table method
- Lagrangian function