Optimality Conditions for Approximate Solutions in Multiobjective Optimization Problems
Ying Gao, Xinmin Yang, Joseph H. W. Lee · Journal of Inequalities and Applications · 2010
We study first- and second-order necessary and sufficient optimality conditions for approximate (weakly, properly) efficient solutions of multiobjective optimization problems. Here, tangent cone, -normal cone, cones of feasible directions, second-order tangent set, asymptotic second-order cone, and Hadamard upper (lower) directional derivatives are used in the characterizations. The results are first presented in convex cases and then generalized to nonconvex cases by employing local concepts.