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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,695 papers · 148 categories

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6 results for “hypomonotone”

On the Hypomonotone Class of Variational Inequalitiesmath.OC

The extragradient method fails for hypomonotone variational inequalities.

problem The convergence of the extragradient method for hypomonotone variational inequalities.

method Application of the extragradient method to hypomonotone linear operators.

result The extragradient method diverges for hypomonotone variational inequalities.

hypomonotone variational inequality extragradient convergence counterexample

2024-10-11abs ↗pdf ↗

Accelerated Extragradient-Type Methods -- Part 2: Generalization and Sublinear Convergence Rates under Co-Hypomonotonicitymath.OC

This paper advances extragradient methods for solving inclusions under co-hypomonotonicity.

problem Solving inclusions with non-Lipschitz mappings.

method Unified and generalized extragradient methods under co-hypomonotonicity.

result Achieved

\mathcal{O}(1/k)

convergence rates for residual norms.

extragradient inclusions co-hypomonotonicity convergence rates

2025-01-08abs ↗pdf ↗

Extragradient-Type Methods with

\mathcal{O} (1/k)

Last-Iterate Convergence Rates for Co-Hypomonotone Inclusionsmath.OC

Two accelerated extragradient methods converge at $O(1/k)$ rate for co-hypomonotone inclusions.

problem Solving co-hypomonotone inclusions with sum of Lipschitz and multivalued operators.

method Developed two Nesterov's accelerated extragradient methods for co-hypomonotone inclusions.

result Achieve

\mathcal{O}(1/k)

last-iterate convergence rates on the residual norm.

co-hypomonotone inclusions extragradient methods Nesterov acceleration last-iterate convergence Lipschitz operators

2023-02-08abs ↗pdf ↗

Variance-Reduced Fast Operator Splitting Methods for Generalized Equationsmath.OC

Develops variance-reduced methods for solving generalized equations.

problem Solving a class of generalized equations, including minimization, minimax, and variational inequalities.

method Integrates accelerated operator splitting, fixed-point methods, and variance reduction techniques.

result Achieves both

\mathcal{O}(1/k^2)

and

o(1/k^2)

convergence rates on the expected squared norm of the FBS residual.

Generalized Equations Operator Splitting Variance Reduction Accelerated Methods Fixed-Point Methods

2025-04-17abs ↗pdf ↗

Sublinear Convergence Rates of Extragradient-Type Methods: A Survey on Classical and Recent Developmentsmath.OC

Survey on extragradient methods for solving nonlinear equations and inclusions.

problem Approximating solutions of nonlinear equations and inclusions.

method Unified convergence analysis of extragradient and its variants.

result Sublinear convergence rates for different classes of algorithms.

extragradient convergence analysis nonlinear equations variational inequalities monotone inclusions

2023-03-30abs ↗pdf ↗

VFOG: Variance-Reduced Fast Optimistic Gradient Methods for a Class of Nonmonotone Generalized Equationsmath.OC

Develops an accelerated algorithm for solving nonmonotone generalized equations.

problem Solving nonmonotone generalized equations with possibly non-accelerated schemes.

method Combines Nesterov's acceleration and variance-reduction techniques for a class of generalized equations.

result Achieves

\mathcal{O}(1/k^2)

convergence rates, improving upon non-accelerated counterparts.

optimistic gradient variance-reduction nonmonotone equations acceleration stochastic variance-reduced schemes

2025-08-22abs ↗pdf ↗