Necessary conditions of nondominated solutions in multicriteria decision making (Q1076612)

We consider multicriteria decision problems in a Banach space whose domination structure is a fixed convex set D. Several equivalence results are derived. If D is an open convex set the above problem is equivalent to a multicriteria decision problem whose domination structure is the tangent cone to D at zero. Further, we obtain a scalar theorem, a Lagrange multiplier theorem and the Kuhn-Tucker condition.