Newton-Type Greedy Selection Methods for $\ell _0$ -Constrained Minimization.

We introduce a family of Newton-type greedy selection methods for $\ell _0$ -constrained minimization problems. The basic idea is to construct a quadratic function to approximate the original objective function around the current iterate and solve the constructed quadratic program over the cardinality constraint. The next iterate is then estimated via a line search operation between the current it...