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Scalable adaptive cubic regularization methods
Adaptive cubic regularization (ARC) methods for unconstrained optimization compute steps from linear systems involving a shifted Hessian in the...
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Cubic Regularization Methods with Second-Order Complexity Guarantee Based on a New Subproblem Reformulation
The cubic regularization (CR) algorithm has attracted a lot of attentions in the literature in recent years. We propose a new reformulation of the...
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Gradient regularization of Newton method with Bregman distances
In this paper, we propose a first second-order scheme based on arbitrary non-Euclidean norms, incorporated by Bregman distances. They are introduced...
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Minimizing Uniformly Convex Functions by Cubic Regularization of Newton Method
In this paper, we study the iteration complexity of cubic regularization of Newton method for solving composite minimization problems with uniformly...
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SCORE: approximating curvature information under self-concordant regularization
Optimization problems that include regularization functions in their objectives are regularly solved in many applications. When one seeks...
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An accelerated first-order method with complexity analysis for solving cubic regularization subproblems
We propose a first-order method to solve the cubic regularization subproblem (CRS) based on a novel reformulation. The reformulation is a constrained...
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Adaptive and local regularization for data fitting by tensor-product spline surfaces
We propose to employ a non-constant regularization weight function (RWF) for data fitting via least-squares tensor-product (TP) spline fitting. In...
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Automatic balancing parameter selection for Tikhonov-TV regularization
This paper considers large-scale linear ill-posed inverse problems whose solutions can be represented as sums of smooth and piecewise constant...
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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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Quadratic regularization methods with finite-difference gradient approximations
This paper presents two quadratic regularization methods with finite-difference gradient approximations for smooth unconstrained optimization...
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On large-scale unconstrained optimization and arbitrary regularization
We present a new algorithm for large-scale unconstrained minimization that, at each iteration, minimizes, approximately, a quadratic model of the...
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A regularization–correction approach for adapting subdivision schemes to the presence of discontinuities
Linear approximation methods suffer from Gibbs oscillations when approximating functions with jumps. Essentially non oscillatory subcell-resolution...
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Restoration of the Product Consumption Rate with Integral Cubic Smoothing Spline, Study of the Best Smoothing Parameter Choice
This article shows how the consumption rate function of a certain customer can be restored from a sequence of discrete purchases. For this, purchases...
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Combining Stochastic Adaptive Cubic Regularization with Negative Curvature for Nonconvex Optimization
We focus on minimizing nonconvex finite-sum functions that typically arise in machine learning problems. In an attempt to solve this problem, the...
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A Second-Order Exponential Time Differencing Multi-step Energy Stable Scheme for Swift–Hohenberg Equation with Quadratic–Cubic Nonlinear Term
In this article, we propose and analyze an energy stable, linear, second-order in time, exponential time differencing multi-step (ETD-MS) method for...
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Solving the Cauchy problem for the Helmholtz equation using cubic smoothing splines
We consider the Cauchy problem for the Helmholtz equation defined in a rectangular domain. The Cauchy data are prescribed on a part of the boundary...
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Cubic Regularized Newton Method for the Saddle Point Models: A Global and Local Convergence Analysis
In this paper, we propose a cubic regularized Newton method for solving the convex-concave minimax saddle point problems. At each iteration, a cubic...
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Simulation of COVID-19 Spread Scenarios in the Republic of Kazakhstan Based on Regularization of the Agent-Based Model
AbstractWe propose an algorithm for modeling scenarios for newly diagnosed cases of COVID-19 in the Republic of Kazakhstan. The algorithm is based...
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Topology-Preserving 3D Image Segmentation Based on Hyperelastic Regularization
Image segmentation is to extract meaningful objects from a given image. For degraded images due to occlusions, obscurities or noises, the accuracy of...
