Abstract
Computational algorithms in mathematical programming have been much in use in the theory of optimal control (see, for example Refs. 1–2). In the present work, we use the algorithm devised by Dinkelback (Ref. 3) for a nonlinear fractional programming problem to prove an existence theorem for a control problem with the cost functional having a fractional form which subsumes the control problem considered by Lee and Marcus (Ref. 4) as a particular case.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Van Slyke, R. M.,Mathematical Programming and Optimal Control, University of California at Berkeley, Ph.D. Thesis, 1965.
Goldstein, A. A.,Convex Programming and Optimal Control, SIAM Journal on Control, Vol. 3, No. 1, 1965.
Dinkelback, W.,On Nonlinear Fractional Programming, Management Science, Vol. 13, No. 7, 1967.
Lee, E. B., andMarkus, L.,Optimal Control for Nonlinear Processes, Archive for Rational Mechanics and Analysis, Vol. 8, No. 1, 1961.
Coddington, E. A., andLevinson, N. L.,Theory of Ordinary Differential Equations, McGraw Hill Book Company, New York, 1955.
Courant, R.,Differential and Integral Calculus, Vol. 2, John Wiley and Sons (Interscience Publishers), New York, 1962.
Author information
Authors and Affiliations
Additional information
Communicated by G. B. Dantzig
The author is thankful to the referee for suggestions.
Rights and permissions
About this article
Cite this article
Bhatt, S.K. An existence theorem for a fractional control problem. J Optim Theory Appl 11, 379–385 (1973). https://doi.org/10.1007/BF00932487
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00932487