Discrete approximations

Wednesday, September 20, 2006 - 1:40pm - 2:30pm
Chris Peterson (Colorado State University)
are natural situations where one is led to consider numeric approximations
of varieties, schemes, sheaves, ideals, modules, etc. For instance, given a
homogeneous ideal one might be able to determine a reduced primary
decomposition via numerical methods (such as homotopy continuation) whereas
symbolic methods might be too slow or not even apply. This provides
motivation to develop a set of tools to handle and manipulate numerically
approximated varieties and schemes. In this talk, I will discuss some tools
Wednesday, November 19, 2008 - 2:45pm - 3:10pm
Todd Munson (Argonne National Laboratory)
Preprocessing technique simplify and strengthen a model prior to calculating a solution. A combination of rules exploiting the constraint set and primal-dual relationships are applied to fix variables, improve their bounds, and eliminate redundant expressions. In addition, some nonconvex constraints can be transformed into convex constraints. Exploiting discrete variables during preprocessing adds rules to identify and exploit special structures and strengthen the formulation prior to computing convex estimators and cuts, and exploring a branch-and-bound tree.
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