## 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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### References:

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