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A global solution strategy for multilevel optimization problems with special non-convexityformulation in the objectives of the inner level problems is presented based on branch-and-bound andmulti-parametric programming approach. An algorithm to such problems is proposed by convexifyingthe 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 program-ming approach. A branch-and-bound procedure is employed until a pre-specied positive tolerance issatised. Moreover, a ϵ-convergence proof is given for the algorithm.