I'm solving an optimization problem in form
$\min \sum x$
subject to,
$ A x = b$ (1)
$ g x \leq d$ (2)
$ x \geq 0$ (3)
Optimization variable is x. The number of rows of A is considerably higher than the number of columns, i.e., the system $Ax = b$ is overdetermined. In equation 2, g and d repesent a nonegative vectors with the proper dimension.
My goal is to find a sparse solution of the problem. I want to find a solution with minimal number of nonzero elements.
Solving the optimization problem only under (1) represents a best basis selection problem that has been solved in literature link.
But what if we add additional constraints (2) and (3), are the any efficient methods to solve the best basis selection problem with (1), (2), and (3)?
