Mixed integer nonlinear programming using interior-point methods

In this paper, we outline a bilevel approach for solving mixed integer nonlinear programming problems. The approach combines a branch-and-bound algorithm in the outer iterations and an infeasible interior-point method in the inner iterations. We report on the details of the implementation, including the efficient pruning of the branch-and-bound tree via equilibrium constraints, warmstart strategies for interior-point methods, and the handling of infeasible subproblems, and present numerical results on a standard problem library. Our goal is to demonstrate the viability of interior-point methods, with suitable modifications, to be used within any MINLP framework, and the numerical results provided are quite encouraging.