Journal of the
Korean Mathematical Society JKMS

Second order necessary optimality condition for properly efficient solutions of a twice differentiable vector optimization problem is given. We obtain a nonsmooth version of the second order necessary optimality condition for properly efficient solutions of a nondifferentiable vector optimization problem. Furthermore, we prove a second order necessary optimality condition for weakly efficient solutions of a nondifferentiable vector optimization problem.

Keywords: vector optimization problem, properly efficient solutions, second order necessary optimality conditions, second order contingent set, second order adjacent set, singular approximate subdifferential, (Mordukhovich) normal cone

MSC numbers: Primary 90C29; Secondary 90C46