@article{publications16696,
          volume = {146},
           month = {August},
          author = {J{\'e}r{\^o}me Bolte and Shoham Sabach and Marc Teboulle},
           title = {Proximal alternating linearized method for nonconvex and nonsmooth problems},
       publisher = {Springer},
         journal = {Mathematical Programming},
           pages = {459--494},
            year = {2014},
             url = {https://publications.ut-capitole.fr/id/eprint/16696/},
        abstract = {We introduce a proximal alternating linearized minimization (PALM) algorithm for solving a broad class of nonconvex and nonsmooth minimization problems. Building on the powerful Kurdyka?{\L}ojasiewicz property, we derive a self-contained convergence analysis framework and establish that each bounded sequence generated by PALM globally converges to a critical point. Our approach allows to analyze various classes of nonconvex-nonsmooth problems and related nonconvex proximal forward?backward algorithms with semi-algebraic problem?s data, the later property being shared by many functions arising in a wide variety of fundamental applications. A by-product of our framework also shows that our results are new even in the convex setting. As an illustration of the results, we derive a new and simple globally convergent algorithm for solving the sparse nonnegative matrix factorization problem.}
}