PARALLEL VARIABLE TRANSFORMATION IN UNCONSTRAINED OPTIMIZATION

A general framework for unconstrained minimization of a nonlinear func tion using parallel processors is presented. The basic idea underlying the proposed parallel variable transformation algorithm is to transfo rm the variables into more than one space of smaller dimension simulta neously and compute candidate solutions on the latter spaces in parall el. The candidate solutions obtained are then used to generate an impr oved solution to the original problem. Global convergence and the line ar rate of convergence of the algorithm are established under suitable conditions. Two recently proposed parallel optimization algorithms, t he parallel gradient distribution (PGD) algorithm and the unconstraine d 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. S pecific algorithmic schemes are also suggested.