Optimality conditions and duality for nondifferentiable multiobjective fractional programming problems with \((C,\alpha ,\rho ,d)\)-convexity (Q630011)

The authors consider a class of nondifferentiable multi-objective fractional programming problems in which each component of the objective function contains a term involving the support function of a compact convex set. For the investigations in this paper, \((C, \alpha \rho, d)\)-convexity is assumed which has been recently introduced by \textit{D. H. Yuan, X. L. Liu, A. Chinchuluun} and \textit{P. M. Pardalos} [J. Optim. Theory Appl. 129, No. 1, 185--199 (2006; Zbl 1146.90077)]. Under this assumption, some sufficient optimality conditions (Section 3) and (weak and strong) duality results (Section 4) for weakly efficient solutions of such problems are derived. The results of this paper generalize previous results given by \textit{D. S. Kim, S. J. Kim} and \textit{M. H. Kim} [J. Optim. Theory Appl. 129, No. 1, 131--146 (2006; Zbl 1149.90135)] and \textit{X.-J. Long, N.-J. Huang} and \textit{Z.-B. Liu} [J. Ind. Manag. Optim. 4, No. 2, 287--298 (2008; Zbl 1161.90480)].