# 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

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topCharnes, 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

top- 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
- 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
- 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
- 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
- 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
- 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)
- 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
- 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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