In this paper we provide new randomized algorithms with improved runtimes for solving
linear programs with two-sided constraints. In the special case of the minimum cost flow …

The Forster transform is a method of regularizing a dataset by placing it in radial isotropic
position while maintaining some of its essential properties. Forster transforms have played a …

Given a separation oracle SO for a convex function f that has an integral minimizer inside a
box with radius R, we show how to efficiently find a minimizer of f using at most O (n (n+ log …

Given a convex function $ f $ on $\mathbb {R}^ n $ with an integer minimizer, we show how
to find an exact minimizer of $ f $ using $ O (n^ 2\log n) $ calls to a separation oracle and …

Given a convex function f on ℝ n with an integer minimizer, we show how to find an exact
minimizer of f using O (n 2 log n) calls to a separation oracle and O (n 4 log n) time. The …

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

In breakthrough work, Tardos (Oper. Res.'86) gave a proximity based framework for solving
linear programming (LP) in time depending only on the constraint matrix in the bit complexity …

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 …

It is an open question to determine if the theory of self-concordant barriers can provide an
interior point method with strongly polynomial complexity in linear programming. In the …

Whereas interior point methods provide polynomial-time linear programming algorithms, the
running time bounds depend on bit-complexity or condition measures that can be …