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First and second order optimality conditions in vector optimization. (English) Zbl 0722.90065
This paper provides a definition of the notion of “regularly lower uniformly differentiable mapping” which contains the Fréchet differentiable mappings and continuous convex mappings. For such mappings the authors present optimality conditions of Fritz-John type, giving a “multiplier rule” for a vector optimization problem with equality and inequality constraints by using an augmented Lagrangian. In the end, by adding a second order differentiability assumption to the necessary, previously obtained conditions, sufficient optimality conditions without convexity or regularity are obtained.

90C29 Multi-objective and goal programming
49J50 Fréchet and Gateaux differentiability in optimization
49K05 Optimality conditions for free problems in one independent variable
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