# ON SECOND ORDER NECESSARY OPTIMALITY CONDITIONS FOR VECTOR OPTIMIZATION PROBLEMS

• Lee, Gue-Myung ;
• Kim, Moon-Hee
• Published : 2003.03.01
• 72 14

#### Abstract

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

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2. Parameter-free duality models and applications to semiinfinite minmax fractional programming based on second-order ( $$\phi ,\eta ,\rho ,\theta ,{\tilde{m}}$$ ϕ , η , ρ , θ , m ~ )-sonvexities 2017, https://doi.org/10.1007/s12597-017-0323-8
3. vol.18, pp.4, 2003, https://doi.org/10.4134/CKMS.2003.18.4.587
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