| Title:
|
Semi-infinite programming, differentiability and geometric programming: Part II (English) |
| Author:
|
Charnes, Abraham |
| Author:
|
Cooper, William Wager |
| Author:
|
Kortanek, Kenneth O. |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
14 |
| Issue:
|
1 |
| Year:
|
1969 |
| Pages:
|
15-22 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
operations research |
| MSC:
|
90-60 |
| idZBL:
|
Zbl 0191.48801 |
| idMR:
|
MR0270756 |
| DOI:
|
10.21136/AM.1969.103204 |
| . |
| Date available:
|
2008-05-20T17:44:09Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103204 |
| . |
| Reference:
|
[1] Arrow K. J. L. Hurwicz, Uzawa H.: Constraint Qualifications in Maximization Problems.Naval Research Logistics Quarterly, Vol. 8, No. 2, June 1961. MR 0129481 |
| Reference:
|
[2] Charnes A., and W. W. Cooper: The Strong Minkowski Farkas-Weyl Theorem for Vector spaces over Ordered Fields.Proceedings of Nat. Acad. Sciences, Vol. 44, No. 9, pp. 914 - 916, Sept. 1958. MR 0142056, 10.1073/pnas.44.9.914 |
| Reference:
|
[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. MR 0157773 |
| Reference:
|
[4] Charnes A., Cooper W. W., Kortanek K.: Duality in Semi-Infinite Programs and Some works of Haar and Caratheodory.Management Science, Vol. 9, No. 2, January, 1963, 209-228. Zbl 0995.90615, MR 0168382, 10.1287/mnsc.9.2.209 |
| Reference:
|
[5] Charnes A., Cooper W. W., Kortanek K.: On Representations of Semi-Infinite Programs Which Have No Duality Gaps.Management Science Vol. 12, No. 1, September, 1965. Zbl 0143.42304, MR 0198976, 10.1287/mnsc.12.1.113 |
| Reference:
|
[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. |
| Reference:
|
[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. |
| Reference:
|
[8] Slater M.: Lagrange Multipliers Revisited: A Contribution to Non-Linear Programming.Cowles Commission Paper, Math. No. 403, New Haven, Nov. 1950. |
| . |
