Geodesic
Tangent Cones and Convexity
Canadian mathematical bulletin, Tome 19 (1976) no. 3, pp. 257-261

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Borwein, J.; O’Brien, R. Tangent Cones and Convexity. Canadian mathematical bulletin, Tome 19 (1976) no. 3, pp. 257-261. doi: 10.4153/CMB-1976-040-x
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[1] 1. Abadie, J., Problèmes d’Optimisation, Institut Blaise Pascal, Paris (1965). Google Scholar

[2] 2. Borwein, J., Weak tangent cones and optimization, to appear. Google Scholar

[3] 3. Day, M. M., Normed Linear Spaces (3rd edition), Springer-Verlag, New York (1973). Google Scholar

[4] 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] 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] 6. Klee, Vol. Extremal structure of convex sets, II, Math. Z., Vol. 69 (1958), 90–104. Google Scholar

[7] 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] 8. Peck, N. T., Support points in locally convex spaces, Duke Math. J. Vol. 38 (1971), 271–278. Google Scholar

[9] 9. Robertson, A. P. and Robertson, W. J., Topological Vector Spaces, Cambridge University Press (1966). Google Scholar

[10] 10. Varaiya, P. P., Nonlinear programming in Banach spaces, SIAM J. Appl. Math., Vol. 19 (1967), 239–244. Google Scholar

[11] 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] 12. Zlobec, S. and Massam, H., Various definitions of the derivative in mathematical programming, Mathematical Programming, Vol. 7 (1974), 144–161. Google Scholar

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