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A Unified Analysis for the Subgradient Methods Minimizing Composite Nonconvex, Nonsmooth and Non-Lipschitz Functions
In this paper we propose a proximal subgradient method (Prox-SubGrad) for solving nonconvex and nonsmooth optimization problems without assuming Lipschitz continuity conditions.
An Augmented Lagrangian Approach to Conically Constrained Non-monotone Variational Inequality Problems
Under an assumption, to be called the primal-dual variational coherence condition in the paper, we prove the convergence of ALAVI.
Revisiting Subgradient Method: Complexity and Convergence Beyond Lipschitz Continuity
In particular, when $f$ is convex, we show $\mathcal{O}(\log(k)/\sqrt{k})$ rate of convergence in terms of the suboptimality gap.
Randomized Coordinate Subgradient Method for Nonsmooth Composite Optimization
For the case when $f$ is weakly convex and its subdifferential satisfies the global metric subregularity property, we derive the $\mathcal{O}(\varepsilon^{-4})$ iteration complexity in expectation.
Randomized Primal-Dual Coordinate Method for Large-scale Linearly Constrained Nonsmooth Nonconvex Optimization
The large-scale linearly constrained nonsmooth nonconvex optimization finds wide applications in machine learning, including non-PSD Kernel SVM, linearly constrained Lasso with nonsmooth nonconvex penalty, etc.
