A nonmonotone line search technique for Newton's method
SIAM Journal on Numerical Analysis
A posteriori error bounds for the linearly-constrained varitional inequality problem
Mathematics of Operations Research
Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Weak sharp minima in mathematical programming
SIAM Journal on Control and Optimization
Dual coordinate ascent methods for non-strictly convex minimization
Mathematical Programming: Series A and B
New error bounds for the linear complementarity problem
Mathematics of Operations Research
New improved error bounds for the linear complementarity problem
Mathematical Programming: Series A and B
Nonlinear complementarity as unconstrained and constrained minimization
Mathematical Programming: Series A and B - Special issue: Festschrift in Honor of Philip Wolfe part II: studies in nonlinear programming
On linear convergence of iterative methods for the variational inequality problem
Proceedings of the international meeting on Linear/nonlinear iterative methods and verification of solution
Parallel Gradient Distribution in Unconstrained Optimization
SIAM Journal on Control and Optimization
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
On the Convergence of Constrained Parallel Variable Distribution Algorithms
SIAM Journal on Optimization
Testing Parallel Variable Transformation
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
Computational Optimization and Applications
Parallel Variable Distribution for Constrained Optimization
Computational Optimization and Applications
Parallel Constrained Optimization via Distribution of Variables
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
On a second order parallel variable transformation approach
The Korean Journal of Computational & Applied Mathematics
A syncro-parallel nonsmooth PGD algorithm for nonsmooth optimization
Journal of Applied Mathematics and Computing
Sprouting search-an algorithmic framework for asynchronous parallel unconstrained optimization
Optimization Methods & Software
A Parallel Implementation of the PBSGDS Method for Solving CBAU Optimization Problems
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
A method for solving the system of linear equations and linear inequalities
Mathematical and Computer Modelling: An International Journal
Hi-index | 0.00 |
We consider the recently proposed parallel variable distribution(PVD) algorithm of Ferris and Mangasarian [4] for solvingoptimization problems in which the variables are distributed amongp processors. Each processor has the primary responsibility forupdating its block of variables while allowing the remaining“secondary” variables tochange in a restricted fashion along some easily computable directions.We propose useful generalizationsthat consist, for the general unconstrained case, of replacing exact global solution ofthe subproblems by a certain natural sufficient descent condition, and,for the convex case, of inexact subproblem solution in thePVD algorithm. These modifications are the key features ofthe algorithm that has not been analyzed before.The proposed modified algorithms are more practical andmake it easier to achieve good load balancing among the parallelprocessors.We present a general framework for the analysis of thisclass of algorithms and derive some new and improved linear convergence resultsfor problems with weak sharp minima of order 2 and strongly convex problems.We also show that nonmonotone synchronization schemesare admissible, which further improves flexibility of PVD approach.