PBLAS
Piecewise basic linear algebra system
Status: ongoing
Description
Numerical linear algebra is vital for almost all numerical algorithms nowadays.
In particular, most numerical optimization algorithms benefit from an efficient implementation of linear algebra,
for example, to represent derivative information used for step direction computation.
However, in the past decades, there has been a growing number of nonsmooth applications, which require new approaches.
These new approaches heavily rely on generalized derivatives
that cannot be represented by standard linear algebra objects like Jacobi matrices.
In this project, we develop a piecewise linear algebra system based on recent developments in Algorithmic Differentiation.
The system can be used to represent and evaluate generalised derivatives in a userfriendly and efficient way.
It allows to easily design new optimization algorithms for nonsmooth optimization problems.
Publications

T. Bosse
:
(Almost) matrixfree solver for piecewise linear functions in absnormal form. in
Numerical Linear Algebra with Applications, 26(5):e2258, 2019.
more ...

T. F. Bosse,
S. H. K. Narayanan
:
Study of the numerical efficiency of structured absnormal forms. in
Optimization Methods and Software, 36(5):909933, 2021.
more ...