A bundle-based proximal descent method achieves O(1/delta^4) for Moreau stationarity on weakly convex functions and adapts to O(1/delta^2) under smoothness and linear convergence under quadratic growth.
Proximal bundle methods for hybrid weakly convex composite optimization problems
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abstract
This paper establishes the iteration-complexity of proximal bundle methods for solving hybrid (i.e., a blend of smooth and nonsmooth) weakly convex composite optimization (HWC-CO) problems. This is done in a unified manner by considering a proximal bundle framework (PBF), which includes various well-known bundle update schemes. In contrast to hard-to-check stationary conditions (e.g., the Moreau stationarity) used by other methods for solving HWC-CO, PBF uses a stationarity measure that is easily verifiable.
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A Proximal Descent Method for Minimizing Weakly Convex Optimization
A bundle-based proximal descent method achieves O(1/delta^4) for Moreau stationarity on weakly convex functions and adapts to O(1/delta^2) under smoothness and linear convergence under quadratic growth.