An approximate decomposition algorithm for convex minimization

摘要: For nonsmooth convex optimization, Robert Mifflin and Claudia Sagastizabal introduce a VU-space decomposition algorithm in (2005) [11]. An attractive property of this is that if primal-dual track exists, uses bundle subroutine. With the inclusion simple line search, it proved to be globally superlinearly convergent. However, drawback needs exact subgradients objective function, which expensive compute. In paper an approximate based on proximal bundle-type method introduced capable deal with subgradients. It shown sequence iterates generated by resulting converges optimal solutions problem. Numerical tests emphasize theoretical findings.