ICQM is a MATLAB script for approximating the solution to the integer convex quadratic minimization problem. For more information, see our companion paper.

ICQM requires CVX. Our method is based on a semidefinite programming (SDP) relaxation, and uses the MOSEK solver if possible.

The main routine can be invoked with:

[lb, ub, xhat] = ICQM(P, q, r, K)

where the first three arguments P, q, and r describe the convex quadratic function to be minimized on the integer lattice. The fourth argument K is an optional parameter controlling the number of sample points used in the randomized algorithm.

The output parameters lb and ub each gives a lower and upper bound on the optimal value of the problem. The other output xhat is an integer point that attains the objective value of ub.

See the ICQM_example.m file for an example.