Abstract

In this paper (strictly) locally --connected, locally (naturally) quasi --connected and (strictly) locally pseudo --connected functions are defined for a vector optimization problem over cones. Involving these functions necessary and sufficient optimality conditions are obtained for an approximate weak quasi efficient solution of this problem. Approximate Wolfe type and Mond-Weir type duals are formulated and duality results are established.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 36
Issue: 1
Year: 2023

DOI: 10.12732/ijam.v36i1.3

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References

1. [1] M. Avriel, I. Zang, Generalized arcwise-connected functions and characterizations of local-global minimum properties, J. Optim. Theory Appl., 32, No 4 (1980), 407-425.
2. [2] G.M. Ewing, Sufficient conditions for global minima of suitably convex functions from variational and control theory, SIAM Rev., 19, No 2 (1977), 202-220.
3. [3] F. Flores-Bazan, N. Hadjisavvas, C. Vera, An optional alternative theorem and applications to mathematical programming, J. Glob. Optim., 37 (2007), 229-243.
4. [4] V. Jeyakumar, First and second order fractional programming duality, Opsearch, 22, No 1 (1985), 24-41.
5. [5] V. Jeyakumar, -convexity and second order duality, Utilitas Math., 29 (1986), 71-85.
6. [6] R.N. Kaul, V. Lyall, S. Kaur, Locally connected set and functions, J. Math. Anal. Appl., 134, No 1 (1988), 30-45.
7. [7] R.N. Kaul and V. Lyall, Locally connected functions and optimality, Indian J. Pure Appl. Math. 22, No 2 (1991), 99-108.
8. [8] R.N. Kaul, S. Kaur, Generalization of convex and related functions, Eur. J. Oper. Res., 9 (1982), 369-377.
9. [9] V. Lyall, S.K. Suneja, S. Aggarwal, Fritz John optimality and duality for non-convex programs, J. Math. Anal. Appl., 212, No 1 (1997), 38-50.
10. [10] J.M. Ortega, W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
11. [11] V. Preda, C. Niculescu, On duality minmax problems involving -locally arcwise connected and related functions, Analele Universitatii Bucuresti Matematica, 49, No 2 (2000), 185-196.
12. [12] V. Preda and C. Niculescu, Optimality conditions and duality for multiobjective programs involving local arcwise connected and generalized connected functions, Rev. Roumaine Math. Pures Appl., 48, No 1 (2003), 61-79. 50 V. Sharma, M. Chaudhary
13. [13] I.M. Stancu-Minasian, Fractional Programming, Theory, Methods and Applications , Kluwer Academic Publishers, Dordrecht, 1997.
14. [14] I.M. Stancu-Minasian, Duality for nonlinear fractional programming involving generalized locally arcwise connected functions, Rev. Roumaine Math. Pures Appl., 49, No 3 (2004), 289-301.
15. [15] I.M. Stancu-Minasian, Optimality conditions for nonlinear programming with generalized locally arcwise connected functions, Proc. Romanian Acad. Ser A, 5(2) (2004), 123-127.
16. [16] I.M. Stancu-Minasian, Optimality and duality in nonlinear programming involving semilocally B-preinvex and related functions, Eur. J. Oper. Res. 173 (2006), 47-58.
17. [17] I.M. Stancu-Minasian and A. Madalina, Sufficient optimality conditions for nonlinear programming with -locally arcwise connected and related functions, Nonlinear Analysis Forum 13, No 1 (2008), 85-93.
18. [18] S.K. Suneja, S. Sharma, M. Chaudhary, Vector Optimization with generalized cone locally connected function, Opsearch, 55, No 2 (2018), 302-319.
19. [19] J.P. Vial, Strong and Weak convexity of sets and functions, Math. Oper. Res., 8, No 2 (1983), 231-259.