| Title:
|
Qualitative analysis of basic notions in parametric convex programming. I. Parameters in the constraints (English) |
| Author:
|
Osman, Mohamed Sayed Ali |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
22 |
| Issue:
|
5 |
| Year:
|
1977 |
| Pages:
|
318-332 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper presents a qualitative analysis of basic notions in parametric convex programming for convex programs with parameters in the righthand sides of the constraints. These notions are the set of feasible parameters, the solvability set and the stability sets of the first and of the second kind. The functions encountered in the paper are assumed to possess first order partial continuous derivatives on $R^n$, the parameters assume arbitrary real values and therefore the results obtained in the paper can be used for a wide class of convex programs. () |
| MSC:
|
90C25 |
| MSC:
|
90C31 |
| idZBL:
|
Zbl 0383.90097 |
| idMR:
|
MR0449692 |
| DOI:
|
10.21136/AM.1977.103710 |
| . |
| Date available:
|
2008-05-20T18:07:57Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103710 |
| . |
| Reference:
|
[1] Abadie J.: On the Kuhn-Tucker theorem.in J. Abadie (ed.) "Nonlinear Programming", pp. 21 - 36, North Holland Publishing Company, Amsterdam, 1967. Zbl 0183.22803, MR 0218116 |
| Reference:
|
[2] Boot J. C. G.: On sensitivity analysis in convex quadratic programming.Op. Research, 11, 771 - 786 (1963). MR 0154747, 10.1287/opre.11.5.771 |
| Reference:
|
[3] Daniel J. W.: Stability of the solution of definite quadratic programs.Math. Programming, 5, 41-53 (1973). Zbl 0269.90037, MR 0449681, 10.1007/BF01580110 |
| Reference:
|
[4] Dantzig G. B., Folkman J., Shapiro N.: On the continuity of the minimum set of a continuous function.J. Math. Anal, and Appl. 17, 519-548 (1967). Zbl 0153.49201, MR 0207426, 10.1016/0022-247X(67)90139-4 |
| Reference:
|
[5] Dieudonne J.: Foundations of modern analysis.New York: Academic Press 1960. Zbl 0100.04201, MR 0120319 |
| Reference:
|
[6] Evans J. P., Gould F. J.: Stability in nonlinear programming.Op. Research, 18, 107-118 (1970). Zbl 0232.90057, MR 0264984, 10.1287/opre.18.1.107 |
| Reference:
|
[7] Guddat J.: Stabilitätsuntersuchungen in der quadratischen parametrischen Optimierung.Dissertation. Zur Erlagung des akademischen Grades (dr. Sc. nat.), Humboldt Universität, Berlin, 1974. |
| Reference:
|
[8] Mangasarian O. L.: Nonlinear Programming.McGraw-Hill, Inc., New York, London, 1969. Zbl 0194.20201, MR 0252038 |
| Reference:
|
[9] Nožička F., Guddat J., Hollatz H., Bank B.: Theorie der linearen parametrischen Optimierung.Akademie-Verlag, Berlin, 1974. |
| Reference:
|
[10] Rockafellar R. T.: Duality and Stability in Extremum Problems Involving Convex Functions.Pacific J. of Math. 21, 167-187 (1967). Zbl 0154.44902, MR 0211759, 10.2140/pjm.1967.21.167 |
| Reference:
|
[11] Rockafellar R. T.: Convex Analysis.Princeton, Princeton University Press, 1969. MR 1451876 |
| Reference:
|
[12] Stoer J., Witzgall Ch.: Convexity and Optimization in Finite Dimensions I.Berlin, Heidelberg, New York, 1970. MR 0286498 |
| . |
