Zeroth-Order Algorithms for Smooth Saddle-Point Problems

Domain Decomposition Algorithms for Saddle Point Problems

In this paper, we introduce some domain decomposition methods for saddle point problems with or without a penalty term, such as the Stokes system and the mixed formulation of linear elasticity. We also consider more general nonsymmetric problems, such as the Oseen system, which are no longer saddle point problems but can be studied in the same abstract framework which we adopt. Several approach...

Frank-Wolfe Algorithms for Saddle Point Problems

We extend the Frank-Wolfe (FW) optimization algorithm to solve constrained smooth convex-concave saddle point (SP) problems. Remarkably, the method only requires access to linear minimization oracles. Leveraging recent advances in FW optimization, we provide the first proof of convergence of a FW-type saddle point solver over polytopes, thereby partially answering a 30 year-old conjecture. We a...

L ∞ - convergence of saddle - point approximations for second order problems

Multilevel Gradient Uzawa Algorithms for Symmetric Saddle Point Problems

In this paper, we introduce a general multilevel gradient Uzawa algorithm for symmetric saddle point systems. We compare its performance with the performance of the standard Uzawa multilevel algorithm. The main idea of the approach is to combine a double inexact Uzawa algorithm at the continuous level with a gradient type algorithm at the discrete level. The algorithm is based on the existence ...

Residual reduction algorithms for nonsymmetric saddle point problems

In this paper, we introduce and analyze Uzawa algorithms for non-symmetric saddle point systems. Convergence for the algorithms is established based on new spectral results about Schur complements. A new Uzawa type algorithm with optimal relaxation parameters at each new iteration is introduced and analyzed in a general framework. Numerical results supporting the efficiency of the algorithms ar...