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On higher-order proto-differentiability and higher-order asymptotic proto-differentiability of weak perturbation maps in parametric vector optimization. (English) Zbl 1527.90232

Summary: The main purpose of this paper is to study higher-order sensitivity analysis in parametric vector optimization problems. Firstly, the higher-order proto-differentiability/the higher-order asymptotic proto-differentiability of the feasible map of a parametric vector optimization problem are considered. Then, we verify that the weak efficient solution map and the weak perturbation map of a parameterized vector optimization problem are higher-order proto-differentiable/higher-order asymptotic proto-differentiable under some suitable qualification conditions.

MSC:

90C31 Sensitivity, stability, parametric optimization
90C29 Multi-objective and goal programming
90C46 Optimality conditions and duality in mathematical programming
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