Chambolle–Pock’s Primal-Dual Method with Mismatched Adjoint

The Randomized Kaczmarz Method with Mismatched Adjoint

This paper investigates the randomized version of the Kaczmarz method to solve linear systems in the case where the adjoint of the system matrix is not exact—a situation we refer to as “mismatched adjoint”. We show that the method may still converge both in the overand underdetermined consistent case under appropriate conditions, and we calculate the expected asymptotic rate of linear convergen...

Dual-Primal FETI Method

The FETI algorithms are numerically scalable iterative domain decomposition methods. These methods are well documented for solving equations arising from the Finite Element discretization of second or fourth order elasticity problems. The one level FETI method equipped with the Dirichlet preconditioner was shown to be numerically scalable for second order elasticity problems while the two level...

Warm Start of the Primal - Dual Method

A practical warm-start procedure is described for the infeasible primal-dual interior-point method employed to solve the restricted master problem within the cutting-plane method. In contrast to the theoretical developments in this eld, the approach presented in this paper does not make the unrealistic assumption that the new cuts are shallow. Moreover, it treats systematically the case when a ...

The primal-dual method for approximation algorithms

In this survey, we give an overview of a technique used to design and analyze algorithms that provide approximate solutions to NP -hard problems in combinatorial optimization. Because of parallels with the primal-dual method commonly used in combinatorial optimization, we call it the primal-dual method for approximation algorithms. We show how this technique can be used to derive approximation ...

Approximation Algorithms: The Primal-Dual Method