Professor Xiyin Zheng was invited to give a lecture

发布时间: 2023-03-20 00:46:03

Topic：Slater Condition for Tangent Derivatives

Speaker：Xiyin Zheng  Yunnan University

Time：2022-06-22  09:30-10:30

Location：Tencent Meeting

Introduction：

Noting that the usual Slater condition is not applicable in nonconvex optimization,we introduce the Slater condition for the Bouligand and Clarke tangent derivatives of a general (not necessarily convex) vector-valued function F with respect to a closed convex cone. Under the Slater condition of the Clarke tangent derivative of a vector-valued function F, it is proved that the normal cone of the sublevel set of F at a reference point can be formulated by the subdi erential of F at the same reference point. Without any assumption, it is proved that the Slater condition of the Bouligand tangent derivative is always stable when the objective function undergoes small calm perturbations. Based on this, we prove that the Slater condition of the Bouligand tangent derivative of a vector-valued function F is sufficient for F to have a stable error bound when F undergoes small calm Clarke-regular perturbations. In the composite-convexity case, it is also proved to be necessary. Moreover, we give some quantitative formulae for error bound moduli. Our results are new even in the case of scalar-valued functions.