Journal
MATHEMATICAL PROGRAMMING
Volume 106, Issue 2, Pages 225-236Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s10107-005-0594-3
Keywords
Mixed-Integer Programs; valid inequalities; Unit Commitment problem; portfolio optimization
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We show that the convex envelope of the objective function of Mixed-Integer Programming problems with a specific structure is the perspective function of the continuous part of the objective function. Using a characterization of the subdifferential of the perspective function, we derive perspective cuts, a family of valid inequalities for the problem. Perspective cuts can be shown to belong to the general family of disjunctive cuts, but they do not require the solution of a potentially costly nonlinear programming problem to be separated. Using perspective cuts substantially improves the performance of Branch & Cut approaches for at least two models that, either naturally or after a proper reformulation, have the required structure: the Unit Commitment problem in electrical power production and the Mean-Variance problem in portfolio optimization.
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