This book gathers threads that have evolved across different mathematical disciplines into
seamless narrative. It deals with condition as a main aspect in the understanding of the …

It is undeniable that geometric ideas have been very important to the foundations of modern
discrete optimization. The influence that geometric algorithms have in optimization was …

We prove that primal-dual log-barrier interior point methods are not strongly polynomial, by
constructing a family of linear programs with 3r+1 inequalities in dimension 2r for which the …

Algebraic statistics exploits the use of algebraic techniques to develop new paradigms and
algorithms for data analysis. The development of computational algebra software provides a …

Tropical geometry has been recently used to obtain new complexity results in convex
optimization and game theory. In this paper, we present an application of this approach to a …

We study properties and applications of various circuit imbalance measures associated with
linear spaces. These measures describe possible ratios between nonzero entries of support …

The Hurwitz form of a variety is the discriminant that characterizes linear spaces of
complementary dimension which intersect the variety in fewer than degree many points. We …

Exponential varieties arise from exponential families in statistics. These real algebraic
varieties have strong positivity and convexity properties, familiar from toric varieties and their …

Entropic regularization is a method for large-scale linear programming. Geometrically, one
traces intersections of the feasible polytope with scaled toric varieties, starting at the Birch …

The Santaló point of a convex polytope is the interior point which leads to a polar dual of
minimal volume. This minimization problem is relevant in interior point methods for convex …