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Necessary conditions for vector optimization in infinite dimension. (English) Zbl 1363.49027

The authors study general second-order necessary conditions satisfied at local weakly efficient points of vector optimization problems in an infinite dimensional space. The vector optimization problems have the form \[ \text{minimize }f(x)\text{ subject to }g(x)\in -K, \] where \(f: X \rightarrow Y\), \(g: X \rightarrow Z\) are given functions, \(X,Y,Z\) are normed linear spaces and \(K\) is a closed convex pointed cone in \(Z\) with non-empty interior. Three theorems establishing necessary conditions of efficiency are presented. Implications of the theorems are compared with each other in the concluding part of the paper.

MSC:

49K10 Optimality conditions for free problems in two or more independent variables
49J52 Nonsmooth analysis
49J50 Fréchet and Gateaux differentiability in optimization
90C29 Multi-objective and goal programming
90C30 Nonlinear programming
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