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A friendly smoothed analysis of the simplex method
TLDR
An improved and simpler analysis of shadow simplex methods, where the main algorithm requires an expected O(d2 √logn σ−2 + d5 log3/2 n) number of simplex pivots, and an improved shadow bound is obtained. Expand
A scaling-invariant algorithm for linear programming whose running time depends only on the constraint matrix
TLDR
A scaling invariant LLS algorithm is developed, which uses and dynamically maintains improving estimates of the circuit ratio digraph, together with a refined potential function based analysis for LLS algorithms in general. Expand
Smoothed Analysis of the Simplex Method
TLDR
This chapter begins the smoothed analysis discussion with an analysis of the successive shortest path algorithm for the minimum-cost maximum-flow problem under objective perturbations, a classical instantiation of the shadow vertex simplex method. Expand
On the Integrality Gap of Binary Integer Programs with Gaussian Data
TLDR
The results give a Gaussian analogue of the classical integrality gap result of Dyer and Frieze in the case of random packing IPs and proves that the gap between the value of the linear programming relaxation and the IP is upper bounded by $\operatorname{poly}(m)(\log n)^2 / n$. Expand
A Friendly Smoothed Analysis of the Simplex Method
TLDR
This presentation explains the excellent practical performance of the simplex method for linear programming and some of the most successful frameworks for understan... Expand
Simple Iterative Methods for Linear Optimization over Convex Sets
TLDR
Simple iterative methods for computing approximately optimal primal and dual solutions for the problem of maximizing a linear functional over a convex set given by a separation oracle are given, based on variants of the classical Von Neumann and Frank-Wolfe algorithms. Expand
Asymptotics Bounds on the Combinatorial Diameter of Random Polytopes
The combinatorial diameter diam(P ) of a polytope P is the maximum shortest-path distance between any pair of vertices. In this paper, we provide upper and lower bounds on the combinatorial diameterExpand