Artículos de revistas
Preinvex Functions And Weak Efficient Solutions For Some Vectorial Optimization Problem In Banach Spaces
Registro en:
Computers And Mathematics With Applications. , v. 48, n. 5-6, p. 885 - 895, 2004.
8981221
10.1016/j.camwa.2003.05.013
2-s2.0-14644415575
Autor
Dos Santos L.B.
Osuna-Gomez R.
Rojas-Medar M.A.
Rufian-Lizana A.
Institución
Resumen
In this work, we introduce the notion of preinvex function for functions between Banach spaces. By using these functions, we obtain necessary and sufficient conditions of optimality for vectorial problems with restrictions of inequalities. Moreover, we will show that this class of problems has the property that each local optimal solution is in fact global. © 2004 Elsevier Ltd. All rights reserved. 48 5-6 885 895 Clarke, F.H., (1983) Optimization and Nonsmooth Analysis, , Wiley New York Craven, B.D., Nonsmooth multiobjective programming (1989) Numer. Funct. Anal. Optimiz., 10, pp. 49-64 Minami, M., Weak Pareto-optimal necessary conditions in a nondifferential multiobjective program on a Banach space (1983) Journal Optim. Theory Appl., 41, pp. 451-461 Mishra, S.K., Mukherjee, R.N., On generalised convex multiobjective nonsmooth programming (1996) Journal of the Australian Mathematical Society Ser B, 38, pp. 140-148 Osuna Gómez, R., Programación con objetivos múltiples: Dualidad (1995) Doctoral Thesis, , Universidad de Sevilla New York Osuna Gómez, R., Rufián-Lizana, A., Ruíz-Canales, P., Multiobjective fractional programming with generalized convexity (2000) Sociedad de Estadística e Investigación Operativa Top 8, 1, pp. 97-110 Osuna-Gómez, R., Beato-Moreno, A., Rufián-Lizana, A., Generalized convexity in multiobjective programming (1999) Journal of Mathematical Analysis and Applications, 233, pp. 205-220 Osuna-Gómez, R., Rufián-Lizana, A., Ruíz-Canales, P., Invex functions and generalized convexity in multiobjective programming (1998) Journal of Optimization Theory and Applications, 98, pp. 651-661 El Abdouni, B., Thibault, L., Lagrange multipliers for Pareto nonsmooth programming problems in Banach spaces (1992) Optimization, 26, pp. 277-285 Coladas, L., Li, Z., Wang, S., Optimality conditions for multiobjective and nonsmooth minimisation in abstract spaces (1994) Bulletin of the Australian Mathematical Society, 50, pp. 205-218 Brandão, A.J.V., Rojas-Medal, M.A., Silva, G.N., Optimality conditions for Pareto nonsmooth nonconvex programming in Banach spaces (1999) Journal Optim. Theory Appl., 103, pp. 65-73 Mangasarian, O.L., (1969) Nonlinear Programming, , McGraw-Hill New York Elster, K.H., Nehse, R., (1980) Optimality Conditions for Some Nonconvex Problems, , Springer-Verlag New York Hanson, M.A., On sufficiency of the Kuhn-Tucker conditions (1981) Journal Mathematical Analysis and Applications, 80, pp. 545-550 Hanson, M.A., Invexity and the Kuhn-Tucker theorem (1999) Journal of Mathematical Analysis and Applications, 236, pp. 594-604 Hanson, M.A., Mond, B., Convex transformable programming problems and invexity (1987) Journal of Information and Optimization Sciences, 8, pp. 201-207 Luenberger, D.G., (1969) Optimization by Vector Spaces Methods, , John Willey & Sons New York Craven, B.D., (1995) Control and Optimization, , Chapman & Hall Dunfort, N., Schwarz, J., (1957) Linear Operators, Part I, , Interscience Girsanov, I.V., (1972) Lectures on Mathematical Theory of Extremum Problems, Lecture Notes in Economics and Mathematical Systems, 67