Mathematical Programming

, Volume 106, Issue 2, pp 225–236 | Cite as

Perspective cuts for a class of convex 0–1 mixed integer programs



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.


Mixed-Integer Programs Valid Inequalities Unit Commitment problem Portfolio Optimization 


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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of PisaPisaItaly
  2. 2.Istituto di Analisi dei Sistemi ed Informatica “Antonio Ruberti”, C.N.R.RomeItaly

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