Geodesic
Optimality Conditions using Approximations for Nonsmooth Vector Optimization Problems under General Inequality Constraints
Journal of convex analysis, Tome 16 (2009) no. 1, pp. 169-186

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First and second-order necessary conditions and sufficient conditions for optimality in nonsmooth vector optimization problems with general inequality constraints are established. We use approximations as generalized derivatives and avoid even continuity assumptions. Convexity conditions are not imposed explicitly. Examples are provided to show that our theorems are easily applied in situations where many known results cannot be. 
@article{JCA_2009_16_1_JCA_2009_16_1_a8,
     author = {P. Q. Khanh and N. D. Tuan},
     title = {Optimality {Conditions} using {Approximations} for {Nonsmooth} {Vector} {Optimization} {Problems} under {General} {Inequality} {Constraints}},
     journal = {Journal of convex analysis},
     pages = {169--186},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2009},
     url = {http://geodesic.mathdoc.fr/item/JCA_2009_16_1_JCA_2009_16_1_a8/}
}
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P. Q. Khanh; N. D. Tuan. Optimality Conditions using Approximations for Nonsmooth Vector Optimization Problems under General Inequality Constraints. Journal of convex analysis, Tome 16 (2009) no. 1, pp. 169-186. http://geodesic.mathdoc.fr/item/JCA_2009_16_1_JCA_2009_16_1_a8/