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Qualitative analysis of basic notions in parametric convex programming. I. (English) Zbl 0383.90097


MSC:

90C31 Sensitivity, stability, parametric optimization
90C25 Convex programming
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References:

[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
[2] Boot J. C. G.: On sensitivity analysis in convex quadratic programming. Op. Research, 11, 771 - 786 (1963).
[3] Daniel J. W.: Stability of the solution of definite quadratic programs. Math. Programming, 5, 41-53 (1973). · Zbl 0269.90037
[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
[5] Dieudonne J.: Foundations of modern analysis. New York: Academic Press 1960. · Zbl 0100.04201
[6] Evans J. P., Gould F. J.: Stability in nonlinear programming. Op. Research, 18, 107-118 (1970). · Zbl 0232.90057
[7] Guddat J.: Stabilitätsuntersuchungen in der quadratischen parametrischen Optimierung. Dissertation. Zur Erlagung des akademischen Grades (dr. Sc. nat.), Humboldt Universität, Berlin, 1974.
[8] Mangasarian O. L.: Nonlinear Programming. McGraw-Hill, Inc., New York, London, 1969. · Zbl 0194.20201
[9] Nožička F., Guddat J., Hollatz H., Bank B.: Theorie der linearen parametrischen Optimierung. Akademie-Verlag, Berlin, 1974. · Zbl 0284.90053
[10] Rockafellar R. T.: Duality and Stability in Extremum Problems Involving Convex Functions. Pacific J. of Math. 21, 167-187 (1967). · Zbl 0154.44902
[11] Rockafellar R. T.: Convex Analysis. Princeton, Princeton University Press, 1969. · Zbl 0193.18401
[12] Stoer J., Witzgall Ch.: Convexity and Optimization in Finite Dimensions I. Berlin, Heidelberg, New York, 1970. · Zbl 0203.52203
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