OPTIMALITY AND DUALITY FOR SET-VALUED FRACTIONAL PROGRAMMING INVOLVING GENERALIZED CONE INVEXITY

S. Sharma; M. Chaudhary

Authors

S. Sharma University of Delhi, Delhi
M. Chaudhary University of Delhi, Delhi

Keywords:

Convex cone, set-valued map, optimality conditions, contingent epiderivative, duality

Abstract

In this paper, a new class of generalized preinvex set-valued maps is introduced and its characterization in terms of their contingent epi-derivatives is obtained. Then we derive necessary and sufficient optimality conditions for a set-valued fractional programming problem using generalized cone invexity. Wolfe and Mond Weir type duals are formulated and various duality results are established.

Author Biographies

S. Sharma, University of Delhi, Delhi

Sunila Sharma is working as Associate Professor in Miranda House, university of Delhi, Delhi. Her area of interest includes vector optimization and generalized convexity.

M. Chaudhary, University of Delhi, Delhi

Mamta Chaudhary is working as Associate Professor in Satyawati College, university of Delhi, Delhi. Currently,
she is perusing her Ph.D. in Mathematics. Her area of interest include vector optimization??and generalized convexity.