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About this paper
Yang Yang, Marius Pesavento, Zhi-Quan Luo, Björn Ottersten
A framework for large-scale nonsmooth nonconvex optimization introduces Inexact Block Successive Convex Approximation (IBSCA) algorithms that guarantee convergence even with inexact subproblem solutions and non-Lipschitz continuous gradients. This approach demonstrates faster convergence and robust performance across challenging signal processing applications such as network anomaly detection and phase retrieval.
Key insights
- Convergence is guaranteed for nonsmooth nonconvex problems without requiring the gradient of the smooth component to be Lipschitz continuous.
- The approximation functions do not need to be global upper bounds of the original objective, allowing for more flexible and problem-specific designs.
- Inexact solutions for the inner-layer approximation subproblems do not compromise outer-layer convergence, eliminating the need for explicit error bounds.
Summary by alphaXiv.
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