TY - JOUR
T1 - The Generalized Jacobian of the Projection onto the Intersection of a Half-Space and a Variable Box
AU - Fang , Sheng
AU - Liu , Yong-Jin
JO - Annals of Applied Mathematics
VL - 4
SP - 379
EP - 390
PY - 2021
DA - 2021/01
SN - 36
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/aam/18583.html
KW - generalized HS Jacobian, projection, intersection of a half-space and a variable box.
AB - <p style="text-align: justify;">This paper is devoted to studying the generalized Jacobian for the projection onto the intersection of a closed half-space and a variable box. This
paper derives the explicit formulas of an element in the set of the generalized
HS Jacobian for the projection. In particular, we reveal that the generalized
HS Jacobian can be formulated as the combination of a diagonal matrix and
few rank-one symmetric matrices, which are crucial for future design of efficient second order nonsmooth methods for solving the related optimization
problems.</p>