programming method penalty quadratic

min x^T Ax
Sum[i=1]xi = k, x € (0,1)^n

Consider the followi data:n=5,k=5, and the matrix A is given by

    A=[3 4 6 7 8; 3 6 2 8 9; 1 5 8 3 9; 3 5 8 0 2; 2 2 2 2 2]

How can I programming method penalty quadratic.

Answer 1

[Matt J]

The problem you've shown has only 1 feasible solution x=[1 1 1 1 1], so no programming to do at all. More generally, you would use quadprog.

[John D'Errico]

While Matt is correct, I would add that technically, there is no feasible solution at all, since the solution was supposed to lie in the OPEN 5-cube, (0,1)^n. Quadprog does not handle problems where the boundary is explicitly excluded. +1 anyway.