Implementing Recycling Methods for Linear Systems in Python with an
  Application to Multiple Objective Optimization
Ainara Garcia Sihong Xie Arielle Carr
Sequences of linear systems arise in the predictor-corrector method when
computing the Pareto front for multi-objective optimization. Rather than
discarding information generated when solving one system, it may be
advantageous to recycle information for subsequent systems. To accomplish this,
we seek to reduce the overall cost of computation when solving linear systems
using common recycling methods. In this work, we assessed the performance of
recycling minimum residual (RMINRES) method along with a map between
coefficient matrices. For these methods to be fully integrated into the
software used in Enouen et al. (2022), there must be working version of each in
both Python and PyTorch. Herein, we discuss the challenges we encountered and
solutions undertaken (and some ongoing) when computing efficient Python
implementations of these recycling strategies. The goal of this project was to
implement RMINRES in Python and PyTorch and add it to the established Pareto
front code to reduce computational cost. Additionally, we wanted to implement
the sparse approximate maps code in Python and PyTorch, so that it can be
parallelized in future work.