Piecewise basic linear algebra system

Status: ongoing



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 non-smooth 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 user-friendly and efficient way. It allows to easily design new optimization algorithms for non-smooth optimization problems.


  • T. Bosse : (Almost) matrix-free solver for piecewise linear functions in abs-normal 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 abs-normal forms. in Optimization Methods and Software, 36(5):909-933, 2021. more ...