Two parallel distribution algorithms for convex constrained minimization problems
The aim of this paper is to study problems, whose objective functions are convex. A nonsmooth constrained parallel gradient distribution (PGD) algorithm is constructed based on a technique due to \textit{Y. R. He} [J. Optimization Theory Appl. 111, 137--153 (2001; Zbl 0987.90067)] where directions and stepsizes in subproblems are obtained via a certain method of solving quadratic programming and the procedure of Armijio type. This algorithm is similar in spirit to the classical block Jacobi and coordinate descent methods. Main result: The PGD algorithm is significantly different from those methods in that each subproblem in the parallelization phase needs to be solved only approximately, for example, by executing a single descent iteration. In a parallel variable distribution (PVD) algorithm, the variables are distributed among processors, each processor not only has primary responsibility for updating its own block of variables but also allows the other secondary variables to change in a restricted manner. A nonsmooth inexact PVD algorithm, in which the solutions of subproblems in the parallel step of the algorithm need not necessarily to be exact is proposed. The authors establish the convergence of this algorithm under some assumptions.
parallel gradient distribution algorithm
scientific article; zbMATH DE number 5162031
scientific article