Coordinate projected gradient descent minimization and its application to orthogonal nonnegative matrix factorization

Flavia Chorobura; Daniela Lupu; Ion Necoara

doi:10.1109/cdc51059.2022.9992996

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arXiv · 2504.00770

Coordinate projected gradient descent minimization and its application to orthogonal nonnegative matrix factorization

Flavia Chorobura·Daniela Lupu·Ion Necoara

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Abstract

In this paper we consider large-scale composite nonconvex optimization problems having the objective function formed as a sum of three terms, first has block coordinate-wise Lipschitz continuous gradient, second is twice differentiable but nonseparable and third is the indicator function of some separable closed convex set. Under these general settings we derive and analyze a new cyclic coordinate descent method, which uses the partial gradient of the differentiable part of the objective, yielding a coordinate gradient descent scheme with a novel adaptive stepsize rule. We prove that this stepsize rule makes the coordinate gradient scheme a descent method, provided that additional assumptions hold for the second term in the objective function. We also present a worst-case complexity analysis for this new method in the nonconvex settings. Numerical results on orthogonal nonnegative matrix factorization problem also confirm the efficiency of our algorithm.

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Flavia Chorobura, Daniela Lupu, Ion Necoara. 2025-04-01. Coordinate projected gradient descent minimization and its application to orthogonal nonnegative matrix factorization. https://doi.org/10.1109/cdc51059.2022.9992996

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