2 Methods 2 2.1 Lagrange Multiplier Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Pegging Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Interior-Point Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3.1 Optimality Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3.2 Interior-Point Algorithm ....

Hardware information: Any computer with a FORTRAN 77 compiler.

We present complexity results on solving real-number standard linear programs LP (A,b, c), where the constraint matrix A ∈ IRm×n, the right-hand-side vector b ∈ IR and the objective coefficient vector c ∈ IR are real. In particular, we present a two-layered interior-point method and show that LP (A,b,0), i.e., the linear feasibility problem Ax = b and x ≥ 0, can be solved in in O(n2.5c(A)) inte...

We present an algorithm for the constrained saddle point problem with a convexconcave function L and convex sets with nonempty interior. The method consists of moving away from the current iterate by choosing certain perturbed vectors. The values of gradients of L at these vectors provide an appropriate direction. Bregman functions allow us to define a curve which starts at the current iterate ...

Abstract. Sampling points from the uniform distribution on a polytope is a well-studied problem, and is an important ingredient in several computational tasks involving polytopes, such as volume estimation. This is achieved by setting up a random walk inside the polytope, with its stationary distribution being uniform in the interior of the polytope. Kannan-Narayanan [6] and Narayanan [9] propo...

The paper is a simplified exposition of an early combined phase I-phase II method for linear programming. The method works from an infeasible start. Besides, there is no need for regularity conditions if the method is applied to a primal-dual formulation.

Let D ∼= 1. In [36, 36, 28], the main result was the extension of universally Gauss scalars. We show that ∆a,t is standard and Gaussian. It is not yet known whether Λ̂ = p ′′, although [36, 4] does address the issue of uniqueness. Here, completeness is clearly a concern.