Semi-infinite programming, differentiability and geometric programming: Part II

Abraham Charnes; William Wager Cooper; Kenneth O. Kortanek

Aplikace matematiky (1969)

  • Volume: 14, Issue: 1, page 15-22
  • ISSN: 0862-7940

Abstract

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The authors deal with a certain specialization of their theory of duality on the case where the objective function is simple continuously differentiable and convex on the set K of the admissible solutions and the constraint functions defining K are continuously differentiable and concave. Further, a way is shown how to generalize the account to the case where the constraint functions of the problem are simple piecewise differentiable and concave. The obtained conditions can be considered as a generalization of Kuhn-Tucher’s theorem.

How to cite

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Charnes, Abraham, Cooper, William Wager, and Kortanek, Kenneth O.. "Semi-infinite programming, differentiability and geometric programming: Part II." Aplikace matematiky 14.1 (1969): 15-22. <http://eudml.org/doc/14574>.

@article{Charnes1969,
abstract = {The authors deal with a certain specialization of their theory of duality on the case where the objective function is simple continuously differentiable and convex on the set $K$ of the admissible solutions and the constraint functions defining $K$ are continuously differentiable and concave. Further, a way is shown how to generalize the account to the case where the constraint functions of the problem are simple piecewise differentiable and concave. The obtained conditions can be considered as a generalization of Kuhn-Tucher’s theorem.},
author = {Charnes, Abraham, Cooper, William Wager, Kortanek, Kenneth O.},
journal = {Aplikace matematiky},
keywords = {operations research},
language = {eng},
number = {1},
pages = {15-22},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Semi-infinite programming, differentiability and geometric programming: Part II},
url = {http://eudml.org/doc/14574},
volume = {14},
year = {1969},
}

TY - JOUR
AU - Charnes, Abraham
AU - Cooper, William Wager
AU - Kortanek, Kenneth O.
TI - Semi-infinite programming, differentiability and geometric programming: Part II
JO - Aplikace matematiky
PY - 1969
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 14
IS - 1
SP - 15
EP - 22
AB - The authors deal with a certain specialization of their theory of duality on the case where the objective function is simple continuously differentiable and convex on the set $K$ of the admissible solutions and the constraint functions defining $K$ are continuously differentiable and concave. Further, a way is shown how to generalize the account to the case where the constraint functions of the problem are simple piecewise differentiable and concave. The obtained conditions can be considered as a generalization of Kuhn-Tucher’s theorem.
LA - eng
KW - operations research
UR - http://eudml.org/doc/14574
ER -

References

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  1. Arrow K. J. L. Hurwicz, Uzawa H., Constraint Qualifications in Maximization Problems, Naval Research Logistics Quarterly, Vol. 8, No. 2, June 1961. (1961) Zbl0129.34103MR0129481
  2. Charnes A., and W. W. Cooper, 10.1073/pnas.44.9.914, Proceedings of Nat. Acad. Sciences, Vol. 44, No. 9, pp. 914 - 916, Sept. 1958. (1958) Zbl0202.03501MR0142056DOI10.1073/pnas.44.9.914
  3. Charnes A., and W. W. Cooper, Management Models and Industrial Applications of Linear Programming, Vols. I and II, New York, J. Wiley and Sons, 1961. (1961) Zbl0107.37004MR0157773
  4. Charnes A., Cooper W. W., Kortanek K., 10.1287/mnsc.9.2.209, Management Science, Vol. 9, No. 2, January, 1963, 209-228. (1963) Zbl0995.90615MR0168382DOI10.1287/mnsc.9.2.209
  5. Charnes A., Cooper W. W., Kortanek K., 10.1287/mnsc.12.1.113, Management Science Vol. 12, No. 1, September, 1965. (1965) Zbl0143.42304MR0198976DOI10.1287/mnsc.12.1.113
  6. Kortanek K., Duality, Semi-Infinite Programming, and Some Aspects of Control in Business and Economic Systems, Ph. D. Thesis, Northwestern University, Evanston, III., 1964. (1964) 
  7. Kuhn H. W., Tucker A. W., Non-Linear Programming, Proc. 2nd Berkeley Symp. Math. Stat. and Prob., J. Neyman (ed.), U. Calif. Press, Berkeley, Calif., 1951, pp. 481-492. (1951) Zbl0044.05903
  8. Slater M., Lagrange Multipliers Revisited: A Contribution to Non-Linear Programming, Cowles Commission Paper, Math. No. 403, New Haven, Nov. 1950. (1950) 

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