Global solution of bilevel programs with a nonconvex inner program
Journal of Global Optimization
A review of recent advances in global optimization
Journal of Global Optimization
Global solution of nonlinear mixed-integer bilevel programs
Journal of Global Optimization
A dynamic convexized method for nonconvex mixed integer nonlinear programming
Computers and Operations Research
Generalized McCormick relaxations
Journal of Global Optimization
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A rigorous decomposition approach to solve separable mixed-integer nonlinear programs where the participating functions are nonconvex is presented. The proposed algorithms consist of solving an alternating sequence of Relaxed Master Problems (mixed-integer linear program) and two nonlinear programming problems (NLPs). A sequence of valid nondecreasing lower bounds and upper bounds is generated by the algorithms which converge in a finite number of iterations. A Primal Bounding Problem is introduced, which is a convex NLP solved at each iteration to derive valid outer approximations of the nonconvex functions in the continuous space. Two decomposition algorithms are presented in this work. On finite termination, the first yields the global solution to the original nonconvex MINLP and the second finds a rigorous bound to the global solution. Convergence and optimality properties, and refinement of the algorithms for efficient implementation are presented. Finally, numerical results are compared with currently available algorithms for example problems, illuminating the potential benefits of the proposed algorithm.