I have the following problem:
Min $c^Tx$
Subject to:
$Ax = b$
$x >= 0 $
Where A is an M x N matrix:
But rather a single solution I would like to know the first K best solutions where $1<= k <= u$ where u is the number of points on the polyhedron $Ax = b$
For example, if k = 2
I would like to know the first optimal point and then second most optimal point.
Can this be done in polytime with respect to the data used to present the problem and the value of k: