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Feasibility-Based Bounds Tightening via Fixed Points

Feasibility-Based Bounds Tightening via Fixed Points,10.1007/978-3-642-17458-2_7,Pietro Belotti,Sonia Cafieri,Jon Lee,Leo Liberti

Feasibility-Based Bounds Tightening via Fixed Points  
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The search tree size of the spatial Branch-and-Bound algo- rithm for Mixed-Integer Nonlinear Programming depends on many fac- tors, one of which is the width of the variable ranges at every tree node. A range reduction technique often employed is called Feasibility Based Bounds Tightening, which is known to be practically fast, and is thus de- ployed at every node of the search tree. From time to time, however, this technique fails to converge to its limit point in finite time, thereby slow- ing the whole Branch-and-Bound search considerably. In this paper we propose a polynomial time method, based on solving a linear program, for computing the limit point of the Feasibility Based Bounds Tightening algorithm applied to linear equality and inequality constraints.
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