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Journal of Convex Analysis 16 (2009), No. 1, 169--186
Copyright Heldermann Verlag 2009

Optimality Conditions using Approximations for Nonsmooth Vector Optimization Problems under General Inequality Constraints

Phan Quoc Khanh
Dept. of Mathematics, International University, Linh Trung - Thu Duc, Hochiminh City, Vietnam

N. D. Tuan
Dept. of Mathematics, University of Natural Sciences, 227 Nguyen Van Cu - D.5, Hochiminh City, Vietnam

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.

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