Subdifferentials of perturbed distance functions in Banach spaces

Authors:
Jin-Hua Wang;Chong Li;Hong-Kun Xu
Affiliations:
Department of Mathematics, Zhejiang University of Technology, Hangzhou, People's Republic of China 310032;Department of Mathematics, Zhejiang University, Hangzhou, People's Republic of China 310027;Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan 804
Venue:
Journal of Global Optimization
Year:
2010

Citing 6
Cited 0

A Gauss-Newton approach to solving generalized inequalities

Mathematics of Operations Research
Nonsmooth analysis and control theory

Nonsmooth analysis and control theory
Proximal Analysis and the Minimal Time Function

SIAM Journal on Control and Optimization
On various notions of regularity of sets in nonsmooth analysis

Nonlinear Analysis: Theory, Methods & Applications
The subgradient formula for the minimal time function in the case of constant dynamics in Hilbert space

Journal of Global Optimization
Limiting subgradients of minimal time functions in Banach spaces

Journal of Global Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

In general Banach space setting, we study the perturbed distance function $${d_S^J(\cdot)}$$ determined by a closed subset S and a lower semicontinuous function J (·). In particular, we show that the Fréchet subdifferential and the proximal subdifferential of a perturbed distance function are representable by virtue of corresponding normal cones of S and subdifferentials of J (·).