Subgradient regularization builds stable descent directions for nonsmooth marginal functions, provably converges to stationary points, and recovers the prox-linear method as a special case.
Approximating subdifferentials by random sampling of gradients
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Subgradient Regularization: A Descent-Oriented Subgradient Method for Nonsmooth Optimization
Subgradient regularization builds stable descent directions for nonsmooth marginal functions, provably converges to stationary points, and recovers the prox-linear method as a special case.