Parallel Constrained Optimization via Distribution of Variables

Abstract

In the parallel variable distribution (PVD) approach for solving optimization problems, the variables are distributed among parallel processors with each processor having the primary responsibility for updating its block of variables while allowing the remaining “secondary” variables to change in a restricted fashion along some easily computable directions. For constrained nonlinear programs, convergence in [4] was established in the special case of convex block-separable constraints. In [11], the PVD approach was extended to problems with general convex constraints by means of utilizing the projected gradient directions for the change of secondary variables. In this paper, we propose two new variants of PVD for the constrained case. For the case of block-separable constraints, we develop a parallel sequential quadratic programming algorithm. This is the first PVD-type method which does not assume convexity of the feasible set for convergence. For inseparable convex constraints, we propose a PVD method based on suitable approximate projected gradient directions. Using such approximate directions is especially important when the projection operation is computationally expensive.

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