A gradient-mapping type stationarity measure built from limiting subdifferentials and proximity operators characterizes Fréchet and proximal stationarity through asymptotic vanishing, and yields an affirmative answer to an open question about proximal gradient cluster points.
A proximal variable smoothing for minimiza- tion of nonlinearly composite nonsmooth function–maxmin dispersion and mimo applications
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abstract
We propose a proximal variable smoothing algorithm for a nonsmooth optimization problem whose cost function is the sum of three functions including a weakly convex composite function. The proposed algorithm has a single-loop structure inspired by a proximal gradient-type method. More precisely, the proposed algorithm consists of two steps: (i) a gradient descent of a time-varying smoothed surrogate function designed partially with the Moreau envelope of the weakly convex function; (ii) an application of the proximity operator of the remaining function not covered by the smoothed surrogate function. For the proposed algorithm, we present a subsequential convergence guarantee in terms of a stationary point, and a convergence rate ${O}(\epsilon^{-3})$ for achieving an $\epsilon$-stationary point. Numerical experiments demonstrate the effectiveness of the proposed algorithm in two scenarios: (i) robust target localization and (ii) multiple-input-multiple-output (MIMO) signal detection.
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math.OC 2years
2026 2roles
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A variable smoothing method for DC composite optimization is proposed for robust phase retrieval, with convergence to DC critical points and experiments indicating better outlier robustness than ℓ1 loss.
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Asymptotic Analysis of Gradient Mapping-type Stationarity Measure for the Sum of Nonconvex Nonsmooth Functions and Applications to Proximal Gradient-type Algorithms
A gradient-mapping type stationarity measure built from limiting subdifferentials and proximity operators characterizes Fréchet and proximal stationarity through asymptotic vanishing, and yields an affirmative answer to an open question about proximal gradient cluster points.
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A DC Composite Optimization via Variable Smoothing for Robust Phase Retrieval with Nonconvex Loss Functions
A variable smoothing method for DC composite optimization is proposed for robust phase retrieval, with convergence to DC critical points and experiments indicating better outlier robustness than ℓ1 loss.