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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
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Category: math
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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
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Date available: 2008-05-20T18:07:57Z
Last updated: 2020-07-28
Stable URL: http://hdl.handle.net/10338.dmlcz/103710
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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
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