On the Approximability of Minimizing Nonzero Variables or Unsatisfied Relations in Linear Systems

@article{Amaldi1998OnTA,
title={On the Approximability of Minimizing Nonzero Variables or Unsatisfied Relations in Linear Systems},
author={Edoardo Amaldi and Viggo Kann},
journal={Theor. Comput. Sci.},
year={1998},
volume={209},
pages={237-260}
}

We investigate the computational complexity of two closely related classes of combinatorial optimization problems for linear systems which arise in various elds such as machine learning, operations research and pattern recognition. In the rst class (Min ULR) one wishes, given a possibly infeasible system of linear relations, to nd a solution that violates as few relations as possible while satisfying all the others. In the second class (Min RVLS) the linear system is supposed to be feasible andâ€¦Â CONTINUE READING