Introduces HOME-DC smoothing for DC functions, derives an inexact first-order oracle, and proposes convergent inexact descent methods with preliminary numerical support on sparse clustering.
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Proximal point algorithm achieves O(ε^{-1}) complexity for quasar-convex functions and linear convergence with O(ln(ε^{-1})) for strongly quasar-convex functions.
Robust learning problems are formulated as quasar-convex optimization, and HiPPA is proposed as an inexact high-order proximal method with global and superlinear convergence guarantees.
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Difference-of-Convex Optimization via Inexact Smoothing Descent Methods: Difference of High-Order Moreau Envelopes
Introduces HOME-DC smoothing for DC functions, derives an inexact first-order oracle, and proposes convergent inexact descent methods with preliminary numerical support on sparse clustering.
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Extending Linear Convergence of the Proximal Point Algorithm: The Quasar-Convex Case
Proximal point algorithm achieves O(ε^{-1}) complexity for quasar-convex functions and linear convergence with O(ln(ε^{-1})) for strongly quasar-convex functions.
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Robust Learning Meets Quasar-Convex Optimization: Inexact High-Order Proximal-Point Methods
Robust learning problems are formulated as quasar-convex optimization, and HiPPA is proposed as an inexact high-order proximal method with global and superlinear convergence guarantees.