On Lagrange-Kuhn-Tucker multipliers for multiobjective optimization problems

Optimization

Volumn 41, Issue 2, 1997, Pages 159-172

  Amahroq, T ^a   Taa, A ^a  

^a FACULTÉ DES SCIENCES ET TECHNIQUES GUÉLIZ   (Morocco)

Author keywords

Convex multifunction; Lagrange Fritz John multipliers; Lagrange Kuhn Tucker multipliers; Metric regularity; Multiobjective optimization

Indexed keywords

EID: 0031461816     PISSN: 02331934     EISSN: None     Source Type: Journal    
DOI: 10.1080/02331939708844332     Document Type: Article

References (17)

1. Amahroq, T., Jourani, A. and Thibault, L., A General Metric Regularity for Multifunction in Asplund Banach Spaces, Preprint.
2. Amahroq, T. and Taa, A., Optimality Conditions for Multiobjective Optimization Problems with γ-paraconvex Data, To appear.
3. Breckner, W. W. (1994). Derived Sets in Multiobjective Optimization, Zeitschrift Analysis und ihre Anwendungen, 13, pp. 725-738.
4. Ciligot-Travain, M. On Lagrange-Kuhn-Tucker Multipliers for Pareto Optimization Problems, Numer. Fund. Anal. and Optimiz., 15, pp. 689-693.
5. Cilogot-Travain, M. (1994). On Fritz-John Multipliers for Pareto Optimization Problems, to appear (see also his thesis, (Faculté des Sciences de Pau 1994)).
6. Clarke, F. H. (1983). Optimization and Nonsmooth Analysis, Wiley-Interscience New-York.
7. Corley, H. W. (1988). Optimality Conditions for Maximization of Set-Valued Functions, Journal of Optimization Theory and Applications, 58, pp. 1-10.
8. El Abdouni, B. and Thibault, L. Conditions d'Optimalité pour les Problèmes d'Optimisation de Pareto dont les Objectifs sont des Multiapplications, To appear. (This paper is in El Abdouni's Thesis, 1995 (thèse de Doctorat d'etat, Université Mohamed V. Faculté des Sciences Rabat)).
9. Hiriart-Urruty, J. B. (1979). Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces, Math. Ope. Res., 4, pp. 79-97.
10. Ioffe, A. D. (1989). Approximate Subdifferentials and Applications III: The Metric Theory, Mathematika, 36, pp. 1-38.
11. Jourani, A. and Thibault. L., Approximate Subdifferentials of Composite Functions. Bulletin of Australian Mathematical Society. To appear.
12. Jourani, A. (1993). Formules d'Intersection dans un Espace de Banach, C. R. A. S. Paris, 317, pp. 825-828.
13. Minami, M. (1983). Weak Pareto-Optimal Necessary Conditions in a Nondifferentiable Multiobjective Program on Banach Space. JOTA, 41, pp. 451-461.
14. Penot, J. P. (1984). Differentiability of Relations and Differential Stability of Perturbed Optimization Problems, SIAM Journal on Control and Optimization, 22, pp. 529-551.
15. Swartz, C. (1987). Pschenichnyis' Theorem for Vector Optimization, Journal of Optimization Theory and Application, 53, pp. 309-317.
16. Taa, A. (1996). Necessary and Sufficient Conditions for Multiobjective Optimization Problems, Optimization. 36, pp. 97-104.
17. Thibault, L. (1990). Lagrange-Kuhn-Tucker Multipliers for Pareto Optimization Problems. Optimization and Nonlinear Analysis Editor Ioffe, Marcus and Reich, Pitman Research Notes in Mathematics Series.