Seminars in Computing and Software
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PhD Thesis Proposal Defense
Date: 2017-06-26 Time: 09:30:00 Room: ITB 225
Finding optimal allocations of resources, scheduling tasks, and designing prototypes are a few of the areas operations research is concerned with. In many cases, these problems can be formulated or approximated as linear optimization problems, which involve maximizing or minimizing a linear function over a domain defined by a set of linear inequalities. The simplex and primal-dual interior point methods are currently the most computationally successful algorithms for linear optimization. While the simplex methods follow an edge path, the interior point methods follow the central path. The algorithmic issues are closely related to the structure of the associated feasible region formed by all feasible solutions. Finding a good bound on the maximal edge-diameter of a polytope in terms of its dimension and the number of its facets is historically closely connected with the theory of the simplex method, as the diameter of the associated feasible region is a lower bound for the number of pivots required in the worst case. Considering bounded feasible regions whose vertices are rational-valued, the proposal investigates a similar question where the number of facets is replaced by the grid embedding size. ======
Contact(s): Antoine Deza