Optimality and duality in fractional multiple objective programming involving semilocally preinvex and related functions

Journal of Mathematical Analysis and Applications

Volumn 288, Issue 2, 2003, Pages 365-382

  Preda, Vasile ^a  

^a UNIVERSITY OF BUCHAREST   (Romania)

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EID: 0346973099     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(02)00460-2     Document Type: Article

References (44)

1. T. Antczak, (p, r)-invex sets and functions, J. Math. Anal. Appl. 263 (2001) 355-379.
2. C.R. Bector, M.K. Bector, J.E. Klassen, Duality for a nonlinear programming problem, Utilitas Math. 11 (1977) 87-89.
3. A. Ben-Israel, B. Mond, What is invexity?, J. Austral. Math. Soc. Ser. B 28 (1986) 1-9.
4. G. Bitran, Duality in nonlinear multiple criteria optimization problems, J. Optim. Theory Appl. 35 (1981) 509-515.
5. A. Cambini, L. Martein, An approach to optimality conditions in vector and scalar optimization, in: Diewert, Spremann, Stehling (Eds.), Mathematical Modelling in Economics, Springer-Verlag, 1993.
6. A. Cambini, L. Martein, Generalized concavity and optimality conditions in vector and scalar optimization, in: Komlosi, et al. (Eds.), Generalized Convexity, in: Lecture Notes in Economics and Mathematical Systems, Vol. 405, Springer-Verlag, 1994.
7. B.D. Corley, Duality theory for maximization with respect to cones, J. Math. Anal. Appl. 84 (1981) 560-568.
8. B.D. Craven, Strong vector minimization and duality, Z. Angew. Math. Mech. 60 (1980) 1-5.
9. B.D. Craven, On quasidifferentiable optimization, J. Austral. Math. Soc. Ser. A 41 (1986) 64-78.
10. K.H. Elster, R. Nehse, Optimality Conditions for Some Nonconvex Problems, Springer-Verlag, New York, 1980.
11. C.M. Ewing, Sufficient conditions for global minima of suitable convex functions from variational and control theory, SIAM Rev. 19 (1977) 202-220.
12. A.M. Geoffrion, Proper efficiency and the theory of vector maximization, J. Math. Anal. Appl. 22 (1968) 618-630.
13. M.A. Hanson, B. Mond, Convex transformable programming problems and invexity, J. Inform. Optim. Sci. 8 (1987) 179-189.
14. M. Hayashi, H. Komiya, Perfect duality for convexlike programs, J. Optim. Theory Appl. 38 (1982) 179-189.
15. G. Heal, Equivalence of saddle-points and optima for non-concave programs, Adv. Appl. Math. 5 (1984) 398-415.
16. E.H. Ivanov, R. Nehse, Some results on dual vector optimization problems, Math. Oper. Statist. Ser. Optim. 16 (1985) 505-517.
17. V. Jeyakumar, Convexlike alternative theorems and mathematical programming, Optimization 16 (1985) 505-517.
18. V. Jeyakumar, Equivalence of saddle-points and optima for and duality for a class of non-smooth non-convex problems, J. Math. Anal. Appl. 130 (1988) 334-343.
19. V. Jeyakumar, Composite nonsmooth programming with Gateaux differentiability, SIAM J. Optim. 1 (1991) 30-41.
20. V. Jeyakumar, B. Mond, On generalized convex mathematical programming, J. Austral. Math. Soc. Ser. B 34 (1992) 43-53.
21. V. Jeyakumar, X.Q. Yang, Convex composite multi-objective nonsmooth programming, Math. Programming 59 (1993) 325-343.
22. R.N. Kaul, S. Kaur, Generalizations of convex and related functions, European J. Oper. Res. 9 (1982) 369-377.
23. R.N. Kaul, S. Kaur, Sufficient optimality conditions using generalized convex functions, Opsearch 19 (1982) 212-224.
24. R.N. Kaul, S. Kaur, Generalized convex functions - properties, optimality and duality, Technical report SOL, 84-4, Stanford University, California, 1984.
25. X.F. Li, J.L. Dong, Subvexormal functions and subvex functions, J. Optim. Theory Appl. 103 (1999) 675-704.
26. V. Lyall, S. Suneja, S. Aggarwal, Optimality and duality in fractional programming involving semilocally convex and related functions, Optimization 41 (1997) 237-255.
27. D.G. Mahajanm, M.N. Vartak, Generalizations of some duality theorems in nonlinear programming, Math. Programming 12 (1977) 293-317.
28. O.L. Mangasarian, Nonlinear Programming, McGraw-Hill, New York, 1969.
29. B. Mond, T. Weir, Generalized concavity and duality, in: S. Schaible, W.T. Ziemba (Eds.), Generalized Concavity in Optimization and Economics, Academic Press, New York, 1981, pp. 263-280.
30. S. Mititelu, Invex sets, Math. Rep. 46 (1994) 529-532.
31. V. Preda, Optimality conditions and duality in multiple objective programming involving semilocally convex and related functions, Optimization 36 (1996) 219-230.
32. V. Preda, I.M. Stancu-Minasian, A. Batatorescu, Optimality and duality in nonlinear programming involving semilocally preinvex and related functions, J. Inform. Optim. Sci. 17 (1996).
33. V. Preda, I.M. Stancu-Minasian, Duality in multiple objective programming involving semilocally preinvex and related functions, Glas. Mat. 32 (1997) 153-165.
34. C. Singh, Duality theory in multiobjective differentiable programming, J. Inform. Optim. Sci. 9 (1988) 231-240.
35. S.K. Suneja, S. Gupta, Duality in nonlinear programming involving semilocally convex and related functions, Optimization 28 (1993) 17-29.
36. T. Tanino, Y. Sawaragi, Duality in multiobjective programming, J. Optim. Theory Appl. 27 (1979) 509-529.
37. T. Weir, Proper efficiency and duality for vector valued optimization problems, J. Austral. Math. Soc. Ser. A 43 (1987) 21-34.
38. T. Weir, B. Mond, Pre-invex functions in multiple objective optimization, J. Math. Anal. Appl. 136 (1988) 29-38.
39. T. Weir, B. Mond, Generalized convexity and duality in multiple objective programming, Bull. Austral. Math. Soc. 39 (1989) 287-299.
40. D.G. White, Vector maximization and Lagrange multipliers, Math. Programming 31 (1985) 192-205.
41. P. Wolfe, Duality theorems for nonlinear programming, Quart. Appl. Math. 19 (1961) 239-244.
42. X.M. Yang, D. Li, On properties of preinvex functions, J. Math. Anal. Appl. 256 (2000) 229-241.
43. X.M. Yang, D. Li, Semistrictly preinvex functions, J. Math. Anal. Appl. 258 (2001) 287-308.
44. X.M. Yang, X.Q. Yang, K.L. Teo, Characterizations and applications of prequasi-invex functions, J. Optim. Theory Appl. 110 (2001) 645-668.