Fast multiple-splitting algorithms for convex optimization (Q2910883)

To solve finite-dimensional convex optimization problems, the authors develop two different classes of general multiple-splitting algorithms based on alternating directions and alternating linearization techniques. Under certain conditions, the complexity bounds on the number of iterations required to obtain an \(\epsilon\)-optimal solution for these algorithms are obtained, namely, \(O(1/\epsilon)\) and \(O(1/\sqrt{\epsilon})\), respectively. Moreover, all algorithms proposed in this paper are parallelizable. Numerical results are presented to demonstrate the computational performance of these algorithms.