The second-order directional derivatives of singular values

2013 ◽  
Vol 43 (2) ◽  
pp. 121-136
Author(s):  
LiWei ZHANG ◽  
XianTao XIAO ◽  
Ning ZHANG
Keyword(s):  
Singular Values ◽  
Second Order ◽  
Directional Derivatives ◽  
Derivatives Of

No Gap Second-order Optimality Conditions for a Matrix Cone Programming Induced by the Nuclear Norm

2016 ◽  
Vol 33 (02) ◽  
pp. 1650010
Author(s):  
Ning Zhang ◽  
Liwei Zhang
Keyword(s):  
Optimality Conditions ◽  
Singular Values ◽  
Second Order ◽  
Nuclear Norm ◽  
Directional Derivatives ◽  
Second Order Optimality Conditions ◽  
The Matrix ◽  
Second Order Tangent Set ◽  
Derivatives Of ◽  
Order Tangent

The first-order and the second-order directional derivatives of singular values are used to characterize the tangent cone, the normal cone and the second-order tangent set of the epigraph of the nuclear norm of matrices. Based on the variational geometry of the epigraph, the no gap second-order optimality conditions for the optimization problem, whose constraint is defined by the matrix cone induced by the nuclear norm, are established.

On second-order directional derivatives of value functions

Optimization ◽  
2013 ◽  
Vol 64 (2) ◽  
pp. 389-407 ◽  
Author(s):  
L. Minchenko ◽  
A. Tarakanov
Keyword(s):  
Second Order ◽  
Directional Derivatives ◽  
Value Functions ◽  
Derivatives Of
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