PROXIMAL DECOMPOSITION OF CONVEX OPTIMIZATION VIA AN ALTERNATING LINEARIZATION ALGORITHM WITH INEXACT ORACLES

In this paper, we consider the optimization problem of minimizing the sum of two convex functions where one objective function phi is assumed to be general and its exact zero -order and first -order information (function values and subgradients) may be difficult to obtain, while the other function phi is expected to be "simple" relatively. An alternating linearization scheme with inexact information is introduced. In this algorithm, two relatively simple subproblems need to be solved in each iteration, and we use an approximate solution instead of an exact form to solve one of the two subproblems. We also prove that the generated sequence converges to a solution of the original problem. Finally, some encouraging numerical experiments are also provided, which show that the inexact scheme has good performance.