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| THE GENERALIZED JACOBIAN OF THE PROJECTION ONTO THE INTERSECTION OF A HALF-SPACE AND A VARIABLE BOX |
| Sheng Fang,Yong-Jin Liu |
| (College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, Fujian, PR China;Key Laboratory of Operations Research and Control of Universities in Fujian, College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, Fujian, PR China) |
| DOI： |
| 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. |
| Key words: generalized HS Jacobian; projection; intersection of a half-space and a variable box |