On multiobjective second order symmetric duality with cone constraints

A pair of Wolfe type multiobjective second order symmetric dual programs with cone constraints is formulated and usual duality results are established under second order invexity assumptions. These results are then used to investigate symmetric duality for minimax version of multiobjective second order symmetric dual programs wherein some of the primal and dual variables are constrained to belong to some arbitrary sets, i.e., the sets of integers. This paper points out certain omissions and inconsistencies in the earlier work of Mishra [S.K. Mishra, Multiobjective second order symmetric duality with cone constraints, European Journal of Operational Research 126 (2000) 675–682] and Mishra and Wang [S.K. Mishra, S.Y. Wang, Second order symmetric duality for nonlinear multiobjective mixed integer programming, European Journal of Operational Research 161 (2005) 673–682].