Distributed asynchronous relaxation methods for convex network flow problems
SIAM Journal on Control and Optimization
Piecewise-linear approximation methods for nonseparable convex optimization
Management Science
Nonlinear functional analysis and its applications
Nonlinear functional analysis and its applications
Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Dual coordinate step methods for linear network flow problems
Mathematical Programming: Series A and B
Parallel optimization for traffic assignment
Mathematical Programming: Series A and B
Partially asynchronous, parallel algorithms for network flow and other problems
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Mathematical Programming: Series A and B
Decomposition algorithm for convex differentiable minimization
Journal of Optimization Theory and Applications
Relaxation methods for problems with strictly convex costs and linear constraints
Mathematics of Operations Research
Asynchronous iterative algorithms: models and convergence
Advances in parallel algorithms
Scientific computing: an introduction with parallel computing
Scientific computing: an introduction with parallel computing
Partial linearization methods in nonlinear programming
Journal of Optimization Theory and Applications
A class of gap functions for variational inequalities
Mathematical Programming: Series A and B
PVM: Parallel virtual machine: a users' guide and tutorial for networked parallel computing
PVM: Parallel virtual machine: a users' guide and tutorial for networked parallel computing
Asynchronous Iterative Methods for Multiprocessors
Journal of the ACM (JACM)
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Computer Architecture and Parallel Processing
Computer Architecture and Parallel Processing
Parallel Computers Two: Architecture, Programming and Algorithms
Parallel Computers Two: Architecture, Programming and Algorithms
A convergent decomposition algorithm for support vector machines
Computational Optimization and Applications
On the convergence of the block nonlinear Gauss-Seidel method under convex constraints
Operations Research Letters
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This paper presents a unified analysis of decomposition algorithmsfor continuously differentiable optimization problems defined onCartesian products of convex feasible sets. The decompositionalgorithms are analyzed using the framework of cost approximationalgorithms. A convergence analysis is made for three decompositionalgorithms: a sequential algorithm which extends the classicalGauss-Seidel scheme, a synchronized parallel algorithm which extendsthe Jacobi method, and a partially asynchronous parallelalgorithm. The analysis validates inexact computations in both thesubproblem and line search phases, and includes convergence rateresults. The range of feasible step lengths within each algorithm isshown to have a direct correspondence to the increasing degree ofparallelism and asynchronism, and the resulting usage of moreoutdated information in the algorithms.