A nonsmooth, nonconvex optimization approach over sphere constraints for Variants of regularized CCA and SVD

Paper Details

Authors: Beck A.; Sharon R.

DOI: 10.3934/JIMO.2026084

Journal: Journal of Industrial and Management Optimization

Year: 2026

Publisher: American Institute of Mathematical Sciences

Document Type: Article

Open Access: All Open Access; Gold Open Access

Cited by: 0

Abstract

In this paper, we study a general nonsmooth, nonconvex optimization problem over a cross product of spheres, suitable for various well-known variants of the canonical correlation analysis (CCA) and singular value decomposition (SVD) problems that promote sparsity and smoothness. We propose an alternating minimization algorithm for a smooth approximation of this problem and study its rate of convergence. Numerical experiments demonstrate the potential of the suggested method. © 2026 the Author(s), licensee AIMS Press.

Keywords

alternating minimization; manifold optimization; nonsmooth nonconvex optimization; smooth approximation; sparse CCA; sparse SVD; sphere constraints

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