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This paper develops a method to obtain the optimal value for theregularization coefficient in a general mixed-integer problem (MIP). Thisapproach eliminates the cross-validation performed in the existing penaltytechniques to obtain a proper value for the regularization coefficient. Weobtain this goal by proposing an alternating method to solve MIPs. First, viaregularization, we convert the MIP into a more mathematically tractable form.Then, we develop an iterative algorithm to update the solution along with theregularization (penalty) coefficient. We show that our update procedureguarantees the convergence of the algorithm. Moreover, assuming the objectivefunction is continuously differentiable, we derive the convergence rate, alower bound on the value of regularization coefficient, and an upper bound onthe number of iterations required for the convergence. We use a radio accesstechnology (RAT) selection problem in a heterogeneous network to benchmark theperformance of our method. Simulation results demonstrate near-optimality ofthe solution and consistency of the convergence behavior with obtainedtheoretical bounds.

No Cross-Validation Required: An Analytical Framework for Regularized Mixed-Integer Problems (Extended Version)