On the Aubin property of a class of parameterized variational systems

On the Aubin property of solution maps to parameterized variational systems with implicit constraints

In the paper a new sufficient condition for the Aubin property to a class of parameterized variational systems is derived. In these systems the constraints depend both on the parameter as well as on the decision variable itself and they include, e.g., parameter-dependent quasi-variational inequalities and implicit complementarity problems. The result is based on a general condition ensuring the Aubin property of implicitly defined multifunctions which employs the recently introduced notion of the directional limiting coderivative. Our final condition can be verified, however, without an explic…

Stability analysis for parameterized variational systems with implicit constraints

In the paper we provide new conditions ensuring the isolated calmness property and the Aubin property of parameterized variational systems with constraints depending, apart from the parameter, also on the solution itself. Such systems include, e.g., quasi-variational inequalities and implicit complementarity problems. Concerning the Aubin property, possible restrictions imposed on the parameter are also admitted. Throughout the paper, tools from the directional limiting generalized differential calculus are employed enabling us to impose only rather weak (non-restrictive) qualification conditi…

$C^2$锥可约集上广义方程的Aubin性质

The Aubin Property for Generalized Equations over $C^2$-cone Reducible Sets

本文确立$C^2$锥可约集上广义方程的Aubin性质与强正则性等价，通过新型指标定理等方法证明，构造反例说明假设不可少，统一推广了三类规划的稳定性结果并消除局部最优性假设。

非线性二阶锥规划的 Aubin 性质与强正则性等价

Aubin Property and Strong Regularity Are Equivalent for Nonlinear Second-Order Cone Programming

本文通过基于 Mordukhovich 判据的约简方法和锥上替代选择引理，证明非线性 SOCP 局部最优解处 Aubin 性质与强正则性等价，并为传统非线性规划的经典等价结果提供新途径。

Sensitivity analysis of variational inequalities via twice epi-differentiability and proto-differentiability of the proximity operator

In this paper we investigate the sensitivity analysis of parameterized nonlinear variational inequalities of second kind in a Hilbert space. The challenge of the present work is to take into account a perturbation on all the data of the problem. This requires special adjustments in the definitions of the generalized first- and second-order differentiations of the involved operators and functions. Precisely, we extend the notions, introduced and thoroughly studied by R.T. Rockafellar, of twice epi-differentiability and proto-differentiability to the case of a parameterized lower semi-continuous…