Symmetric Duality in Complex Spaces over Cones

Abstract

Duality theory plays an important role in optimization theory. Duality theory has been extensively used for many theoretical and computational problems in mathematical programming. In this paper duality results are established for first and second order Wolfe and Mond-Weir type symmetric
dual programs over general polyhedral cones in complex spaces. Corresponding duality relations
for nondifferentiable case are also stated. This work will also remove inconsistencies in the earlier
work in Mishra and Rueda, J. Math. Anal. Appl. 284 (2003) 250-265 and Mishra, Eur. J. Oper.
Res. 127 (2000) 507-518.