Quasar-convex functions admit high-order proximal algorithms with linear convergence for p=2 and superlinear for p>2 under suitable conditions.
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Quasar-Convex Optimization: Fundamental Properties and High-Order Proximal-Point Methods
Quasar-convex functions admit high-order proximal algorithms with linear convergence for p=2 and superlinear for p>2 under suitable conditions.