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The notion of strict minimum of order m for real optimization problems is extended to vector optimization. Its properties and characterization are studied in Ž . the case of finite-dimensional spaces multiobjective problems . Also the notion of super-strict efficiency is introduced for multiobjective problems, and it is proved that, in the scalar case, all of them coincide. Necessary conditions for strict minimality and for super-strict minimality of order m are provided for multiobjective problems with an arbitrary feasible set. When the objective function is Frechet differentiable, necessary and sufficient conditions are established for the case m s 1, resulting in the situation that the strict efficiency and super-strict efficiency notions coincide. ᮊ 2002 Elsevier Science

We study a nonsmooth vector optimization problem with an arbitrary feasible set or a feasible set defined by a generalized inequality constraint and an equality constraint. We assume that the involved functions are nondifferentiable. First, we provide some calculus rules for the contingent derivative in which the stability (a local Lipschitz property at a point) of the functions plays a crucial role. Second, another calculus rules are established for steady functions. Third, necessary optimality conditions are stated using tangent cones to the feasible set and the contingent derivative of the objective function. Finally, some necessary and sufficient conditions are presented through Lagrange multiplier rules.