A multi-parametric programming algorithm for special classes of non-convex multilevel optimization problems

A global solution strategy for multilevel optimization problems with special non-convexity formulation in the objectives of the inner level problems is presented based on branch-and-bound and multi-parametric programming approach. An algorithm to such problems is proposed by convexifying the inner level problem while the variables from upper level problems are considered as parameters. The resulting convex parametric under-estimator problem is solved using multi-parametric programming approach. A branch-and-bound procedure is employed until a pre-specified positive tolerance is satisfied. Moreover, a epsilon -convergence proof is given for the algorithm.