A Parallel Algorithm for a Class of Convex Programs
Shih-Ping Han, Gang Lou · SIAM Journal on Control and Optimization · 1988
A parallel algorithm is proposed in this paper for solving the problem $\min \{ q(x)|x \in C_1 \cap \cdots \cap C_m \} $ where q is an uniformly convex function and $C_i$ are closed convex sets in $R^n$. In each iteration of the method, we solve in parallel m independent subproblems, each minimizing a definite quadratic function over an individual set $C_i$. The method has attractive convergence properties and can be implemented as parallel algorithms for tackling definite quadratic programs, linear programs, systems of linear equations and systems of generalized nonlinear inequalities.