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Tangent Cones and Convexity

Published online by Cambridge University Press:  15 March 2019

J. Borwein  and
R. O’Brien
J. Borwein
Affiliation:
Department of Mathematics, Dalhousie UniversityHalifax, Nova Scotia, Canada B3H 3J5
R. O’Brien
Affiliation:
Department of Mathematics, Dalhousie UniversityHalifax, Nova Scotia, Canada B3H 3J5
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The study of general multiplier theorems (Kuhn-Tucker Conditions) for constrained optimization problems has led to extensions of the notion of a differentiable arc. Abadie [1], Varaiya [10], Guignard [5], Zlobec [11] and Massam [12] investigated the so called cone of tangent vectors to a point in a set for optimization purposes.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 3 , 01 September 1976 , pp. 257 - 261
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Abadie, J., Problèmes d’Optimisation, Institut Blaise Pascal, Paris (1965).Google Scholar
2. Borwein, J., Weak tangent cones and optimization, to appear.Google Scholar
3. Day, M. M., Normed Linear Spaces (3rd edition), Springer-Verlag, New York (1973).Google Scholar
4. Edelstein, M., On nearest points of sets in uniformly convex Banach spaces, J. London Math. Soc., Vol. 43 (1968), 375–377.Google Scholar
5. Guignard, M., Generalized Kuhn-Tucker conditions for mathematical programming problems in Banach space, SIAM J. Control, Vol. 7 (1969), 232–241.Google Scholar
6. Klee, Vol. Extremal structure of convex sets, II, Math. Z., Vol. 69 (1958), 90–104.Google Scholar
7. Kuhn, H. W. and Tucker, A. W., Nonlinear programming, Proc. 2nd Berkeley Symposium on Mathematical Statistics and Probability, Vol. 5, University of California Press, Berkeley (1952), 481–492.Google Scholar
8. Peck, N. T., Support points in locally convex spaces, Duke Math. J. Vol. 38 (1971), 271–278.Google Scholar
9. Robertson, A. P. and Robertson, W. J., Topological Vector Spaces, Cambridge University Press (1966).Google Scholar
10. Varaiya, P. P., Nonlinear programming in Banach spaces, SIAM J. Appl. Math., Vol. 19 (1967), 239–244.Google Scholar
11. Zlobec, S., Asymptotic Kuhn-Tucker conditions for mathematical programming problems ina Banach space, SIAM Control J., Vol. 8 (1970), 505–512.Google Scholar
12. Zlobec, S. and Massam, H., Various definitions of the derivative in mathematical programming, Mathematical Programming, Vol. 7 (1974), 144–161.Google Scholar