Two proximal splitting methods for multi-block separable programming with applications to stable principal component pursuit

摘要: Recent years have witnessed the rapid development of first order methods for multi-block separable programming involving large-scale date-set. The purpose this paper is to introduce two new methods, proximal splitting (PSMs), model under consideration. PSM fully utilizes desired property such problems and adopts Jacobian updating rule, which often results in easy subproblems practice. global convergence worst-case \(\mathcal {O}(1/t)\) rate an ergodic sense are proved condition that involved functions assumed be strongly convex. Applying hybrid Gauss–Seidel rule PSM, we derive second whose can guaranteed only Furthermore, its both non-ergodic senses also established. Finally, numerical on stable principal component pursuit reported testify accuracy speed some comparisons reported.