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On the cones of tangents with applications to mathematical programming.(English)Zbl 0259.90037


MSC:

90C30 Nonlinear programming
90C25 Convex programming

Cite

References:

[1]Bouligand, G.,Introduction à la Géométrie Infinitésimale Directe, Gauthier-Villars, Paris, France, 1932. ·JFM 58.0086.03
[2]Flett, T. M.,Mathematical Analysis, McGraw-Hill, Book Company, New York, New York, 1966. ·Zbl 0177.07801
[3]Flett, T. M.,On Differentiation in Normed Vector Spaces, Journal of the London Mathematical Society, Vol. 42, 1967. ·Zbl 0181.34502
[4]Roetman, E. L.,Tangent Planes and Differentiation, Mathematics Magazine, Vol. 43, No. 1, 1970. ·Zbl 0193.01501
[5]Hestenes, M. R.,Calculus of Variations and Optimal Control Theory, John Wiley and Sons, New York, New York, 1966. ·Zbl 0173.35703
[6]Nashed, M. Z.,Differentiability and Related Properties of Nonlinear Operators: Some Aspects of the Role of Differentials in Nonlinear Functional Analysis, Nonlinear Functional Analysis and Applications, Edited by L. B. Rall, Academic Press, New York, New York, 1971. ·Zbl 0236.46050
[7]Abadie, J.,On the Kuhn-Tucker Theorem, Nonlinear Programming, Edited by J. Abadie, North Holland Publishing Company, Amsterdam, Holland, 1967. ·Zbl 0183.22803
[8]Varaiya, P. P.,Nonlinear Programming in Banach Space, SIAM Journal on Applied Mathematics, Vol. 15, No. 2, 1967. ·Zbl 0171.18004
[9]Guignard, M.,Generalized Kuhn-Tucker Conditions for Mathematical Programming Problems in a Banach Space, SIAM Journal on Control, Vol. 7, No. 12, 1969. ·Zbl 0182.53101
[10]Gould, F. J., andTolle, J. W.,A Necessary and Sufficient Constraint Qualification for Constrained Optimization, SIAM Journal on Applied Mathematics, Vol. 20, No. 2, 1971. ·Zbl 0217.57501
[11]Bazaraa, M. S., Goode, J. J., andShetty, C. M.,Constraint Qualifications Revisited, Management Science, Vol. 18, No. 9, 1972. ·Zbl 0257.90049
[12]Bazaraa, M. S., Goode, J. J., Nashed, M. Z., andShetty, C. M.,Nonlinear Programming Without Differentiability in Banach Spaces: Necessary and Sufficient Constraint Qualification, Applicable Analysis (to appear). ·Zbl 0353.90076
[13]Neustadt, L. W.,A General Theory of Extremals, Journal of Computer and System Sciences, Vol. 3, No. 1, 1969. ·Zbl 0167.08802
[14]Halkin, H.,A Satisfactory Treatment of Equality and Operator Constraints in the Dubovitskii-Milyutin Optimization Formalism, Journal of Optimization Theory and Applications, Vol. 6, No. 2, 1970. ·Zbl 0185.24201
[15]Dubovitskii, A. Ya., andMilyutin, A. A.,Extremum Problems in the Presence of Restrictions, USSR Computational Mathematics and Mathematical Physics, Vol. 5, No. 1, 1965.
[16]Rockafellar, R. T.,Duality and Stability in Extremum Problems Involving Convex Functions, Pacific Journal of Mathematics, Vol. 21, No. 1, 1967. ·Zbl 0154.44902
[17]Rockafellar, R. T.,Duality in Nonlinear Programming, Mathematics of the Decision Sciences, Edited by G. B. Dantzig and A. F. Veinott, American Mathematical Society, Providence, Rhode Island, 1968. ·Zbl 0231.90037
[18]Demyanov, V. F.,Algorithms for Some Minimax Problems. Journal of Computer and System Sciences, Vol. 2, No. 4, 1968. ·Zbl 0177.23104
[19]Demyanov, V. F., andRubinov, A. M.,Approximate Methods for Solving Extremal Problems, American Elsevier Publishing Company, New York, New York, 1970.
[20]Valentine, F. A.,Convex Sets, McGraw-Hill, Book Company, New York, New York, 1964. ·Zbl 0129.37203
[21]Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970. ·Zbl 0193.18401
[22]Van Slyke, R. M., andWets, R. J. B.,A Duality Theorem for Abstract Mathematical Programming with Applications to Optimal Control Theory, Journal of Mathematical Analysis and Applications, Vol. 22, No. 3, 1968. ·Zbl 0157.16004
[23]Brøndsted, A., andRockafellar, R. T.,On Subdifferentiability of Convex Functions, Proceedings of American Mathematical Society, Vol. 16, No. 4, 1965. ·Zbl 0141.11801
[24]Bazaraa, M. S., Goode, J. J., andShetty, C. M.,Optimality Criteria in Nonlinear Programming without Differentiability, Journal of Operations Research, Vol. 19, No. 1, 1971. ·Zbl 0213.45103
[25]Bazaraa, M. S., Goode, J. J., andNashed, M. Z.,Cone Differentiability in Normed Linear Spaces with Applications (to appear). ·Zbl 0241.90056
[26]Mangasarian, O. L.,Nonlinear Programming, McGraw-Hill Book Company, New York, New York, 1969.
[27]Fan, K.,On Systems of Linear Inequalities, Linear Inequalities and Related Systems, Edited by H. W. Kuhn and A. W. Tucker, Annals of Mathematics Study, 38, Princeton University Press, Princeton, New Jersey, 1956. ·Zbl 0072.37602
[28]Hartman, P.,Ordinary Differential Equations, John Wiley and Sons, New York, New York, 1964. ·Zbl 0125.32102
[29]Moreau, J. J.,Fonctionelles Convexes, Lecture Notes, Seminar on Partial Differential Equations, College de France, Montpellier, France, 1966-1967.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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