Optimality conditions for \(C^{1,1}\) vector optimization problems. (English) Zbl 1038.49027

This note deals with the problem of minimizing a vector-valued function \(f: \mathbb{R}^m \to \mathbb{R}^n\), where the order in \(\mathbb{R}^n\) is given by a certain closed convex pointed cone \(K\). The function \(f\) is assumed to be of class \(C^{1,1}\). The authors derive second-order optimality conditions that characterize the efficient solutions and the ideal solutions of this vector-optimization problem. The optimality conditions are based on a suitable concept of second-order subdifferential for \(f\).


49K10 Optimality conditions for free problems in two or more independent variables
49J52 Nonsmooth analysis
90C29 Multi-objective and goal programming
90C46 Optimality conditions and duality in mathematical programming
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