Abstract:We consider a class of composite optimization problems involving a smooth function and a proper, lower semicontinuous regularizer, which may be nonconvex and nonsmooth.
We propose a novel alternating minimization framework that integrates proximal-gradient steps with cubic-regularized Newton updates restricted to a dynamically identified low-dimensional subspace.
Under the Kurdyka--Łojasiewicz (KL) property, we establish global convergence of the proposed method to a stationary point.
Moreover, by incorporating an adaptive thresholding strategy guided by the KL exponent, we prove a finite identification property without imposing any nondegeneracy assumptions.
We further develop a local convergence analysis and show that the proposed method attains a worst-case iteration complexity of $\mathcal{O}(\varepsilon^{-3/2})$ for achieving approximate second-order stationarity.
Numerical experiments on both synthetic and real datasets demonstrate the efficiency and effectiveness of the proposed framework.
From: Min Tao Dr [view email]
[v1]
Tue, 23 Jun 2026 14:02:43 UTC (656 KB)
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