Lagrange multipliers saddle points and scalarizations in composite multiobjective nonsmooth programming

Optimization

Volumn 38, Issue 2, 1996, Pages 93-105

  Mishra, S K ^a  

^a BANARAS HINDU UNIVERSITY   (India)

Author keywords

Composite functions; Lagrange multipliers; Multiobjective problems; Nonsmooth programming; Saddle points; Scalarizations

Indexed keywords

EID: 0040519632     PISSN: 02331934     EISSN: None     Source Type: Journal    
DOI: 10.1080/02331939608844241     Document Type: Article

References (25)

1. Bector, C. R., Chandra, S. and Husain, I. (1994) "Optimality conditions and duality in subdifferentiable multiobiective fractional programming" J. Optim. Theory Appl., 79, 105-126.
2. Bector, C. R., Chandra, S., and Kumar, V. (1994) "Duality for minmax programming involving V-invex functions", Optimization, 30, 93-103.
3. Clarke, F. H. (1983) Optimization and Nonsmooth Analysis, Wiley, New York.
4. Corley, H. W. (1987) "Existence and Lagrangian duality for maximization of set valued functions", J. Optim. Theory and Appl. 54, 489-501.
5. Craven, B. D. (1978) Mathematical Programming and Control Theory, Chapman and Hall, London
6. Craven, B. D. (1990) "Quasimin and quasisaddle point for sector optimization", Numer. Funct. Anal. Optim. 11, 45-54.
7. Egudo, R. R. and Hanson, M. A. (1993) "On sufficiency of Kuhn-Tucker conditions in nonsmooth multiobjective programming", FSU Technical Report No. M-888.
8. Hartley, R. (1985) "Vector and parametric programming", J. Oper. Res. Soc. 36, 423-432.
9. Henig, M. I. (1982) "Proper efficiency with respect to cones", J. Optim. Theory Appl., 36, 387-407.
10. Jahn, J. (1985) "Scalarization in multiobjective optimization", Mathematics of Multiobjective Optimization, Edited by P. Serafini, Springer Verlag, Berlin, Germany, 45-88.
11. Jeyakumar, V. and Mond, B. (1992) "On generalized convex mathematical programming", J. Austral. Math. Soc. Ser. B 34, 43-53.
12. Jeyakumar, V. and Yang, X. Q. (1993) "Convex composite multiobjective nonsmooth programming", Math. Progr. 59, 325-343.
13. Mangasarian, O. L. (1988) "A simple characterization of solution sets of convex programs", Oper. Letters 7, 21-26.
14. Mishra, S. K. and Mukherjee, R. N. (1995) "On generalized convex multiobjective nonsmooth programming", J. Austral. Math. Soc. Ser. B. (to appear).
15. Mishra, S. K. and Mukherjee, R. N. (1995) "Generalized convex composite multiobjective nonsmooth programming and conditional proper efficiency", Optimization (Vol.34, pp 53-66.
16. Mukherjee R. N. and Mishra, S. K. (1994) "Sufficient optimality criteria and duality for multiobjective variational problems with V-invexity", Indian J. Pure Appl. Math., 25(8), 801-813.
17. Nakayama, H. (1984) "Geometric consideration of duality in vector optimization", J. Optim. Theory Appl. 44, 625-655.
18. Rockafellar, R. T. (1969) Convex Analysis (Princeton University Press, Princeton, N. J.).
19. Sawaragi, Y., Nakayama, H. and Tanino, T. (1985) "Theory of Multiobjective Optimization", Academic Press, New York.
20. Tanaka, T. (1988) "Some minimax problems of vector valued functions", J. Optim. Theory Appl. 59, 505-524.
21. Tanaka, T. (1990) "A characterization of generalized saddle points for vector valued functions via scalarization", Nihonkai Math. J. 1, 209-227.
22. Vogel, W. (1974) "Ein Maximum Prinzip für Vector Optimierungs-Aufgaben, Oper. Res. Verfahren, 19, 161-175.
23. Wang, S. Y. (1984) "Theory of the conjugate duality in multiobjective optimization", J. System. Sci. and Math. Sci., 4,. 303-312.
24. Weir, T., Mond, B. and Craven, B. D. (1987) "Weak minimization and duality", Numer. Funct. Anal. Optim. 9, 181-191.
25. Weir, T., Mond, B. and Craven, B. D. (1986) "On duality for weakly minimized vector valued optimization problems", Optimization, 17, 711-721.