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Volume 36, Issue 4
The Generalized Jacobian of the Projection onto the Intersection of a Half-Space and a Variable Box

Sheng Fang & Yong-Jin Liu

Ann. Appl. Math., 36 (2020), pp. 379-390.

Published online: 2021-01

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  • Abstract

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.

  • Keywords

generalized HS Jacobian, projection, intersection of a half-space and a variable box.

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COPYRIGHT: © Global Science Press

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@Article{AAM-36-379, author = {Fang , Sheng and Liu , Yong-Jin}, title = {The Generalized Jacobian of the Projection onto the Intersection of a Half-Space and a Variable Box}, journal = {Annals of Applied Mathematics}, year = {2021}, volume = {36}, number = {4}, pages = {379--390}, abstract = {

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.

}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/18583.html} }
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 -

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.

Sheng Fang & Yong-Jin Liu. (2021). The Generalized Jacobian of the Projection onto the Intersection of a Half-Space and a Variable Box. Annals of Applied Mathematics. 36 (4). 379-390. doi:
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