On necessary and sufficient optimality conditions for multicriterial optimization problems

In this paper, first order necessary and sufficient optimality conditions are derived for nonsmooth optimization problems with multiple criteria. These conditions are given for different optimality notions (i.e. weak, Pareto- and proper minimality) and for different types of derivatives of nonsmooth objective functions (locally Lipschitz continuous and quasidifferentiable) mappings. The conditions are given, if possible, in terms of a derivative and a subdifferential of those mappings.