Decomposition approaches can be used to generate practically efficient solution algorithms for a wide class of optimization problems. For instance, scenario-expanded two-stage stochastic optimization problems can be solved efficiently in practice using Benders Decomposition. The performance of the approach can be influenced by the choice of the cuts that are added during the course of … Read more
We introduce a natural notion of depth that applies to individual cutting planes as well as entire families. This depth has nice properties that make it easy to work with theoretically, and we argue that it is a good proxy for the practical strength of cutting planes. In particular, we show that its value lies … Read more
Semidefinite programming relaxations complement polyhedral relaxations for quadratic optimization, but global optimization solvers built on polyhedral relaxations cannot fully exploit this advantage. This paper develops linear outer-approximations of semidefinite constraints that can be effectively integrated into global solvers. The difference from previous work is that our proposed cuts are (i) sparser with respect to the … Read more