Abstract
We derive a general principle demonstrating that by partitioning the feasible set, the duality gap, existing between a nonconvex program and its lagrangian dual, can be reduced, and in important special cases, even eliminated. The principle can be implemented in a Branch and Bound algorithm which computes an approximate global solution and a corresponding lower bound on the global optimal value. The algorithm involves decomposition and a nonsmooth local search. Numerical results for applying the algorithm to the pooling problem in oil refineries are given.
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Research supported by Shell Laboratorium, Amsterdam, and GIF—The German—Israel Foundation for Scientific Research and Development.
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Ben-Tal, A., Eiger, G. & Gershovitz, V. Global minimization by reducing the duality gap. Mathematical Programming 63, 193–212 (1994). https://doi.org/10.1007/BF01582066
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DOI: https://doi.org/10.1007/BF01582066