Variational sets and asymptotic variational sets of proper perturbation map in parametric vector optimization

On second-order radial-asymptotic proto-differentiability of the borwein perturbation maps

“…Recently, higher-order sensitivity analysis in parametric vector optimization problems and parametric set-valued optimization problems has occupied attention of researchers. In [4,33], some results in higher-order sensitivity analysis have been given by using the higher-order variational sets and asymptotic variational sets. In [13], properties of higher-order contingent-type derivatives of the perturbation and weak perturbation maps of a parameterized optimization problem have been obtained by using the higherorder contingent-type derivatives.…”

On generalized $\tau^w$-contingent epiderivatives in parametric vector optimization problems

“…In primal space approach, the first-order derivatives of perturbation maps were studied in [3,5,7,13,19,26,33]. To get more information, the higher-order derivatives of perturbation maps have been investigated in [1,9,27,29]. Another interesting topic in the primal space approach is to study the proto-differentiability of perturbation maps, introduced in [21].…”