Eigenvalue Blending for Projected Newton

Cheng, Yuan-Yuan; Liu, Ligang; Fu, Xiao-Ming

Eigenvalue Blending for Projected Newton

Files

cgf70027.pdf (54.85 MB)

Date

2025

Authors

Cheng, Yuan-Yuan
Liu, Ligang
Fu, Xiao-Ming

Publisher

The Eurographics Association and John Wiley & Sons Ltd.

Abstract

We propose a novel method to filter eigenvalues for projected Newton. Central to our method is blending the clamped and absolute eigenvalues to adaptively compute the modified Hessian matrix. To determine the blending coefficients, we rely on (1) a key observation and (2) an objective function descent constraint. The observation is that if the quadratic form defined by the Hessian matrix maps the descent direction to a negative real number, the decrease in the objective function is limited. The constraint is that our eigenvalue filtering leads to more reduction in objective function than the absolute eigenvalue filtering [CLL∗24] in the case of second-order Taylor approximation. Our eigenvalue blending is easy to implement and leads to fewer optimization iterations than the state-of-the-art eigenvalue filtering methods.

CCS Concepts: Computing methodologies → Physical simulation

        @article{10.1111:cgf.70027
,
journal = {Computer Graphics Forum},
title = {{Eigenvalue Blending for Projected Newton
}},
author = {Cheng, Yuan-Yuan and 
Liu, Ligang and 
Fu, Xiao-Ming
},
year = {2025
},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.
},
ISSN = {1467-8659
},
DOI = {10.1111/cgf.70027
}
}