Abstract
In this paper we survey recent work on the perspective reformulation approach that generates tight, tractable relaxations for convex mixed integer nonlin- ear programs (MINLP)s. This preprocessing technique is applicable to cases where the MINLP contains binary indicator variables that force continuous decision variables to take the value 0, or to belong to a convex set. We derive from first principles the perspective reformulation, and we discuss a variety of practical MINLPs whose relaxation can be strengthened via the perspective reformulation. The survey concludes with comments and computations comparing various algorithmic techniques for solving perspective reformulations.
AMS(MOS) subject classifications. 90C11, 90C30.
The second author was supported by the US Department of Energy under grants DEFE02-08ER25861 and DE-FG02-09ER25869, and the National Science Foundation under grant CCF-0830153.
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Günlük, O., Linderoth, J. (2012). Perspective Reformulation and Applications. In: Lee, J., Leyffer, S. (eds) Mixed Integer Nonlinear Programming. The IMA Volumes in Mathematics and its Applications, vol 154. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1927-3_3
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DOI: https://doi.org/10.1007/978-1-4614-1927-3_3
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