Minkowski Centers via Robust Optimization: Computation and Applications

Centers of convex sets are geometrical objects that have received extensive attention in the mathematical and optimization literature, both from a theoretical and practical standpoint. For instance, they serve as initialization points for many algorithms such as interior-point, hit-and-run, or cutting-planes methods. First, we observe that computing a Minkowski center of a convex set can … Read more

On the Fermat point of a triangle

For a given triangle $\triangle ABC$, Pierre de Fermat posed around 1640 the problem of finding a point $P$ minimizing the sum $s_P$ of the Euclidean distances from $P$ to the vertices $A$, $B$, $C$. Based on geometrical arguments this problem was first solved by Torricelli shortly after, by Simpson in 1750, and by several … Read more

On the Primal-Dual Geometry of Level Sets in Linear and Conic Optimization

For a conic optimization problem: minimize cx subject to Ax=b, x \in C, we present a geometric relationship between the maximum norms of the level sets of the primal and the inscribed sizes of the level sets of the dual (or the other way around). Citation MIT Operations Research Center Working Paper Article Download View … Read more