Artículos de revistas
Invex Nonsmooth Alternative Theorem And Applications
Registro en:
Optimization. , v. 48, n. 2, p. 239 - 253, 2000.
2331934
2-s2.0-0043059272
Autor
Brandao A.J.V.
Rojas-Medar M.A.
Silva G.N.
Institución
Resumen
An invex constrained nonsmooth optimization problem is considered, in which the presence of an abstract constraint set is possibly allowed. Necessary and sufficient conditions of optimality are provided and weak and strong duality results established. Following Geoffrion's approach an invex nonsmooth alternative theorem of Gordan type is then derived. Subsequently, some applications on multiobjective programming are then pursued. © 2000 OPA (Overseas Publishers Association) N.V. Published by license under the Gordon and Breach Science Publishers imprint. 48 2 239 253 Ben-Israel, A., Mond, B., What is invexity? (1986) J. Austral. Math. Soc. Ser. B, 28, pp. 1-9 Clarke, F.H., Optimization and Nonsmooth Analysis (1990) Classics in Applied Mathematics, 5. , SIAM Craven, B.D., (1995) Control and Optimization, Chapman and Hall Mathematics Series, , London Craven, B.D., Invex Functions and Constrained Local Minima (1981) Bull. Austral. Math. Soc., 24, pp. 357-366 Craven, B.D., Nondifferentiable Optimization by Smooth Approximations (1986) Optimization, 17, pp. 3-17 Craven, B.D., Yang, X.Q., A Nonsmooth Version of Alternative Theorem (1991) Utilitas, 40, pp. 117-128 Geoffrion, A.M., Proper Efficiency and the Theory of Vector Maximization (1968) J. Math. Anal. Appl., 22, pp. 618-630 Geoffrion, A.M., Duality in Nonlinear Programming: A simplified Applications-Oriented Development (1971) SIAM Rev., 13, pp. 1-38 Giorgi, G., Guerraggio, A., Various Types of Nonsmooth Invex Functions (1996) J. Inf. Optim. Sci., 17, pp. 137-150 Hanson, M.A., On sufficiency of the Kuhn-Tucker conditions (1981) J. Math. Anal. Appl., 80, pp. 545-550 Hayashi, M., Komiya, H., Perfect Duality and Convexlike Programs (1980) J. Optim. Theory and Appl., 38, pp. 179-189 Jeyakumar, V., Convexlike Alternative Theorems and Mathematical Programming (1985) Optimization, 16, pp. 643-652 Mangasarian, O.L., Nonlinear Programming (1994) Classics in Applied Mathematics, 10. , SIAM Phuong, T.D., Sach, P.H., Yen, N.D., Strict Lower Semicontinuity of the Level Sets and Invexity of a Locally Lipschitz Function (1995) J. Optim. Theory and Appl., 87, pp. 579-594 Pini, R., Invexity and Generalized Convexity (1991) Optimization, 22, pp. 513-525 Reiland, T.W., Nonsmooth Invexity (1990) Bull. Austral. Math. Soc., 42, pp. 437-446 Weir, T., Mond, B., Pre-Invex Functions in Multiple Objective Optimization (1988) J. Math. Anal. Appl., 136, pp. 29-38