Split cuts are among the most important and well-understood cuts for general mixed-integer programs. In this paper we consider some recent generalizations of split cuts and compare their relative strength. More precisely, we compare the elementary closures of split, cross, crooked cross and general multi-branch split cuts as well as cuts obtained from multi-row and basic relaxations. We present...

Gaussian split Ewald (GSE) is a versatile Ewald mesh method that is fast and accurate when used with both real-space and k-space Poisson solvers. While real-space methods are known to be asymptotically superior to k-space methods in terms of both computational cost and parallelization efficiency, k-space methods such as smooth particle-mesh Ewald (SPME) have thus far remained dominant because t...

3.2 Likelihood equations and errors-in-variables regression; Solari's example.. Here is a case, noted by Solari (1969), where the likelihood equations (3.1.1) have solutions, none of which are maximum likelihood estimates. be observed points in the plane. Suppose we want to do a form of " errors in variables " regression, in other words to fit the data by a straight line, assuming normal errors...

In this paper, we discuss an extension of split cuts that is based on widening the underlying disjunctions. That the formula for deriving intersection cuts based on splits can be adapted to this case has been known for a decade now. For the first time though, we present applications and computational results. We further discuss extensions of the existing theory with respect to cut strengthening...