Synthesis of a k-winners-take-all neural network using linear programming with bounded variables

A k-winners-take-all (KWTA) problem is formulated as a linear programming (LP) problem with bounded variables. The solution set of the LP problem determines the winners. The LP problem is converted into an unconstrained optimization problem with two exact penalty functions, that is solved by using a gradient descent method implemented as a neural network. Theoretical results ensuring the convergence to the correct solution are provided.