PWL for MILP of Quadratic Functions

Definition of Aeq, Beq, Aineq, Bineq to formulate a MILP problem of a quadratic function f(x)=x^2, using Piece-Wise Linearization.

This simple function [f_approx,f,Aeq,beq,Aineq,bineq]=quadaprox_CPLEX(x,xmax,Y) returns the matrices Aeq,beq,Aineq,bineq to formulate a MILP of a Piece-Wise Linearization of the quadratic function f(x)=x^2. It also returns the approximated value f_approx (using the CPLEX library) and the real value f evaluated at x, where xmax is the maximum value of x and Y is the number of PWL pieces.

The MILP problem formulation is presented in the Image.

If you don't use CPLEX to solve MILP, then use the function [Aeq,beq,Aineq,bineq]=quadaprox(P,Pmax,Y), but it won't calculate the approximat value.