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A Multiscale Semi-Smooth Newton Method for Optimal Transport
Our goal is to solve the large-scale linear programming (LP) formulation of Optimal Transport (OT) problems efficiently. Our key observations are:...
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Second order semi-smooth Proximal Newton methods in Hilbert spaces
We develop a globalized Proximal Newton method for composite and possibly non-convex minimization problems in Hilbert spaces. Additionally, we impose...
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Inexact proximal DC Newton-type method for nonconvex composite functions
We consider a class of difference-of-convex (DC) optimization problems where the objective function is the sum of a smooth function and a possibly...
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Inexact Newton Method for Solving Generalized Nash Equilibrium Problems
In this article, we present an inexact Newton method to solve generalized Nash equilibrium problems (GNEPs). Two types of GNEPs are studied: player...
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Gauss Newton Method for Solving Variational Problems of PDEs with Neural Network Discretizaitons
The numerical solution of differential equations using machine learning-based approaches has gained significant popularity. Neural network-based...
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Inexact proximal Newton methods in Hilbert spaces
We consider proximal Newton methods with an inexact computation of update steps. To this end, we introduce two inexactness criteria which...
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On the Application of the SCD Semismooth* Newton Method to Variational Inequalities of the Second Kind
The paper starts with a description of SCD (subspace containing derivative) map**s and the SCD Newton method for the solution of general...
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A smoothing Newton method based on the modulus equation for a class of weakly nonlinear complementarity problems
By equivalently transforming a class of weakly nonlinear complementarity problems into a modulus equation, and introducing a smoothing approximation...
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A trust-region LP-Newton method for constrained nonsmooth equations under Hölder metric subregularity
We describe and analyze a globally convergent algorithm to find a possible nonisolated zero of a piecewise smooth map** over a polyhedral set. Such...
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High-Order CENO Finite-Volume Scheme with Anisotropic Adaptive Mesh Refinement: Efficient Inexact Newton Method for Steady Three-Dimensional Flows
A high-order finite-volume scheme with anisotropic adaptive mesh refinement (AMR) is combined with a parallel inexact Newton method for the solution...
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Riemannian Stochastic Variance-Reduced Cubic Regularized Newton Method for Submanifold Optimization
We propose a stochastic variance-reduced cubic regularized Newton algorithm to optimize the finite-sum problem over a Riemannian submanifold of the...
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On the local convergence of a stochastic semismooth Newton method for nonsmooth nonconvex optimization
In this work, we present probabilistic local convergence results for a stochastic semismooth Newton method for a class of stochastic composite...
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On the core entropy of Newton maps
In this paper, we define the core entropy for postcritically-finite Newton maps and study its continuity within this family. We show that the entropy...
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A path-following inexact Newton method for PDE-constrained optimal control in BV
We study a PDE-constrained optimal control problem that involves functions of bounded variation as controls and includes the TV seminorm of the...
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Unified primal-dual active set method for dynamic frictional contact problems
In this paper, we propose a semi-smooth Newton method and a primal-dual active set strategy to solve dynamical contact problems with friction. The...
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Optimal step length for the Newton method: case of self-concordant functions
The theoretical foundation of path-following methods is the performance analysis of the (damped) Newton step on the class of self-concordant...
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A Corrected Inexact Proximal Augmented Lagrangian Method with a Relative Error Criterion for a Class of Group-Quadratic Regularized Optimal Transport Problems
The optimal transport (OT) problem and its related problems have attracted significant attention and have been extensively studied in various...
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An Overview of Stochastic Quasi-Newton Methods for Large-Scale Machine Learning
Numerous intriguing optimization problems arise as a result of the advancement of machine learning. The stochastic first-order method is the...
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Newton acceleration on manifolds identified by proximal gradient methods
Proximal methods are known to identify the underlying substructure of nonsmooth optimization problems. Even more, in many interesting situations, the...
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