An inexact augmented Lagrangian method for nonsmooth optimization on Riemannian manifold

Abstract

We consider a nonsmooth optimization problem on Riemannian manifold, whose objective function is the sum of a differentiable component and a nonsmooth convex function. We propose a manifold inexact augmented Lagrangian method (MIALM) for the considered problem. The problem is reformulated to a separable form. By utilizing the Moreau envelope, we get a smoothing subproblem at each iteration of the proposed method. Theoretically, under suitable assumptions, the convergence to critical point of the proposed method is established. In particular, under the condition of that the approximate global minimizer of the iteration subproblem could be obtained, we prove the convergence to global minimizer of the origin problem. Numerical experiments show that, the MIALM is a competitive method compared to some existing methods.

arXiv comment25 pages, 2 tables

References in corpus (5)

• Manopt, a Matlab toolbox for optimization on manifolds
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• Compressed Modes for Variational Problems in Mathematics and Physics
• Convergence of inexact descent methods for nonconvex optimization on Riemannian manifolds
• Primal-Dual Optimization Algorithms over Riemannian Manifolds: an Iteration Complexity Analysis

Cited by in corpus (2)

• A Semismooth Newton based Augmented Lagrangian Method for Nonsmooth Optimization on Matrix Manifolds
• An Inexact Manifold Augmented Lagrangian Method for Adaptive Sparse Canonical Correlation Analysis with Trace Lasso Regularization