We are interested in proving optimality conditions for optimization problems. By
means of different second-order tangent sets, various second-order necessary optimality
conditions are obtained for both scalar and vector optimization problems where
the feasible region is given as a set. We present also second-order sufficient optimality
conditions so that there is only a very small gap with the necessary optimality
conditions. As an application we establish second-order optimality conditions of Fritz
John type, Kuhn-Tucker type 1, and Kuhn-Tucker type 2 for a problem with both
inequality and equality constraints and a twice differentiable functions. At the end, a
very general second-order necessary conditions for efficiency with respect to cones is
present and it is applied to smooth and nonsmooth data.
Keywords: Multiobjective programming, second-order tangent sets, constraint qualifications,
second-order optimality conditions, efficient solutions.
