  This paper develops a method to obtain the optimal value for the
regularization coefficient in a general mixed-integer problem (MIP). This
approach eliminates the cross-validation performed in the existing penalty
techniques to obtain a proper value for the regularization coefficient. We
obtain this goal by proposing an alternating method to solve MIPs. First, via
regularization, we convert the MIP into a more mathematically tractable form.
Then, we develop an iterative algorithm to update the solution along with the
regularization (penalty) coefficient. We show that our update procedure
guarantees the convergence of the algorithm. Moreover, assuming the objective
function is continuously differentiable, we derive the convergence rate, a
lower bound on the value of regularization coefficient, and an upper bound on
the number of iterations required for the convergence. We use a radio access
technology (RAT) selection problem in a heterogeneous network to benchmark the
performance of our method. Simulation results demonstrate near-optimality of
the solution and consistency of the convergence behavior with obtained
theoretical bounds.
