A Decomposition-based MINLP Solution Method Using Piecewise Linear Relaxations
نویسندگان
چکیده
A rigorous decomposition-based approach for solution of nonseparable mixedinteger nonlinear programs involving factorable nonconvex functions is presented. The proposed algorithm consists of solving an alternating sequence of Relaxed Master Problems (a Mixed-Integer Linear Program) and nonlinear programming problems. The number of major iterations can be significantly decreased by use of piecewise linear relaxations of the nonconvex functions. The introduction of piecewise linear relaxations improves the lower bound on the problem but increases the number of constraints and binary variables in the Relaxed Master Problem. A sequence of valid nondecreasing lower bounds and upper bounds are generated by the algorithm that converge in a finite number of iterations. Numerical results are presented for example problems, illuminating the potential benefits of the proposed algorithm.
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