OPTIMALITY CONDITIONS AND DUALITY FOR SEMI-INFINITE PROGRAMMING INVOLVING SEMILOCALLY TYPE I-PREINVEX AND RELATED FUNCTIONS

- Journal title : Communications of the Korean Mathematical Society
- Volume 27, Issue 2, 2012, pp.411-423
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2012.27.2.411

Title & Authors

OPTIMALITY CONDITIONS AND DUALITY FOR SEMI-INFINITE PROGRAMMING INVOLVING SEMILOCALLY TYPE I-PREINVEX AND RELATED FUNCTIONS

Jaiswal, Monika; Mishra, Shashi Kant; Al Shamary, Bader;

Jaiswal, Monika; Mishra, Shashi Kant; Al Shamary, Bader;

Abstract

A nondifferentiable nonlinear semi-infinite programming problem is considered, where the functions involved are -semidifferentiable type I-preinvex and related functions. Necessary and sufficient optimality conditions are obtained for a nondifferentiable nonlinear semi-in nite programming problem. Also, a Mond-Weir type dual and a general Mond-Weir type dual are formulated for the nondifferentiable semi-infinite programming problem and usual duality results are proved using the concepts of generalized semilocally type I-preinvex and related functions.

Keywords

multiobjective programming;semi-infinite programming;optimality;duality;

Language

English

References

1.

K. H. Elster and R. Nehse, Optimality Conditions for some Nonconvex Problems, Springer-Verlag, New York, 1980.

2.

G. M. Ewing, Sufficient conditions for global minima of suitably convex functionals from variational and control theory, SIAM Rev. 19 (1977), no. 2, 202-220.

3.

M. A. Hanson and B. Mond, Necessary and sufficient conditions in constrained opti- mization, Report M683, Department of Statistics, Florida State University, Tallahassee, Florida, 1984.

4.

M. A. Hanson, R. Pini, and C. Singh, Multiobjective programming under generalized type I invexity, J. Math. Anal. Appl. 261 (2001), no. 2, 562-577.

5.

M. Hayashi and H. Komiya, Perfect duality for convexlike programs, J. Optim. Theory Appl. 38 (1982), no. 2, 179-189.

6.

R. N. Kaul and S. Kaur, Generalizations of convex and related functions, European J. Oper. Res. 9 (1982), no. 4, 369-377.

7.

S. Kaur, Theoretical studies in mathematical programming, Ph.D. Thesis, University of Delhi, India, 1984.

8.

S. K. Mishra, S. Y. Wang, and K. K. Lai, Multiple objective fractional programming involving semilocally type I-preinvex and related functions, J. Math. Anal. Appl. 310 (2005), no. 2, 626-640.

9.

S. K. Mishra, S. Y. Wang, and K. K. Lai,Generalized Convexity and Vector Optimization, Springer-Verlag, Berlin Heidelberg, 2009.

10.

M. A. Noor, Nonconvex functions and variational inequalities, J. Optim. Theory Appl. 87 (1995), no. 3, 615-630.

11.

V. Preda, Optimality and duality in fractional multiple objective programming involving semilocally preinvex and related functions, J. Math. Anal. Appl. 288 (2003), no. 2, 365-382.

12.

V. Preda and I. M. Stancu-Minasian, Duality in multiple objective programming involv- ing semilocally preinvex and related functions, Glas. Mat. Ser. III 32(52) (1997), no. 1, 153-165.

13.

V. Preda, I. M. Stancu-Minasian, and A. Batatorescu, Optimality and duality in nonlin- ear programming involving semilocally preinvex and related functions, J. Inform. Optim. Sci. 17 (1996), no. 3, 585-596.

14.

N. G. Rueda and M. A. Hanson, Optimality criteria in mathematical programming involving generalized invexity, J. Math. Anal. Appl. 130 (1988), no. 2, 375-385.

15.

T. Weir and B. Mond, Pre-invex functions in multiple objective optimization, J. Math. Anal. Appl. 136 (1988), no. 1, 29-38.