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 method for solving the system of linear equations and linear inequalities
Mathematical and Computer Modelling: An International Journal
| Hi-index | 0.00 |
A general framework for unconstrained minimization of a nonlinear function using parallel processors is presented. The basic idea underlying the proposed parallel variable transformation algorithm is to transform the variables into more than one space of smaller dimension simultaneously and compute candidate solutions on the latter spaces in parallel. The candidate solutions obtained are then used to generate an improved solution to the original problem. Global convergence and the linear rate of convergence of the algorithm are established under suitable conditions. Two recently proposed parallel optimization algorithms, the parallel gradient distribution (PGD) algorithm and the unconstrained parallel variable distribution (PVD) algorithm, are shown to belong to the class of parallel variable transformation (PVT) algorithms. An earlier parallel algorithm called the updated conjugate subspaces (UCS) method is also shown to be a particular case of the PVT algorithm. Specific algorithmic schemes are also suggested.