A convergence-guaranteed Bregman proximal alternating linearized minimization framework for multi-block nonconvex nonsmooth problems, with closed-form updates for penalized orthogonal nonnegative matrix factorization.
Block-coordinate and incremental aggregated proximal gradient methods for nonsmooth nonconvex problems
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abstract
This paper analyzes block-coordinate proximal gradient methods for minimizing the sum of a separable smooth function and a (nonseparable) nonsmooth function, both of which are allowed to be nonconvex. The main tool in our analysis is the forward-backward envelope (FBE), which serves as a particularly suitable continuous and real-valued Lyapunov function. Global and linear convergence results are established when the cost function satisfies the Kurdyka-\L ojasiewicz property without imposing convexity requirements on the smooth function. Two prominent special cases of the investigated setting are regularized finite sum minimization and the sharing problem; in particular, an immediate byproduct of our analysis leads to novel convergence results and rates for the popular Finito/MISO algorithm in the nonsmooth and nonconvex setting with very general sampling strategies. This paper analyzes block-coordinate proximal gradient methods for minimizing the sum of a separable smooth function and a (nonseparable) nonsmooth function, both of which are allowed to be nonconvex. The main tool in our analysis is the forward-backward envelope (FBE), which serves as a particularly suitable continuous and real-valued Lyapunov function. Global and linear convergence results are established when the cost function satisfies the Kurdyka-\L ojasiewicz property without imposing convexity requirements on the smooth function. Two prominent special cases of the investigated setting are regularized finite sum minimization and the sharing problem; in particular, an immediate byproduct of our analysis leads to novel convergence results and rates for the popular Finito/MISO algorithm in the nonsmooth and nonconvex setting with very general sampling strategies.
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2019 1verdicts
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Multi-block Bregman proximal alternating linearized minimization and its application to orthogonal nonnegative matrix factorization
A convergence-guaranteed Bregman proximal alternating linearized minimization framework for multi-block nonconvex nonsmooth problems, with closed-form updates for penalized orthogonal nonnegative matrix factorization.