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Numerical Simulation of Inverse Retrospective Problems for a Nonlinear Heat Equation
AbstractA method is proposed for numerically solving the inverse problem of restoring the initial condition for a nonlinear one-dimensional heat...
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On Regularization of Classical Optimality Conditions in Convex Optimization Problems for Volterra-Type Systems with Operator Constraints
AbstractWe consider the regularization of classical optimality conditions—the Lagrange principle and the Pontryagin maximum principle—in a convex...
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Accelerated Gradient Methods Combining Tikhonov Regularization with Geometric Dam** Driven by the Hessian
In a Hilbert framework, for general convex differentiable optimization, we consider accelerated gradient dynamics combining Tikhonov regularization...
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Convex optimization via inertial algorithms with vanishing Tikhonov regularization: fast convergence to the minimum norm solution
In a Hilbertian framework, for the minimization of a general convex differentiable function f , we introduce new inertial dynamics and algorithms that...
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Regularization of Fourier Series with Approximate Coefficients for the Problem of Phase Probability Density Function Estimation
AbstractThis paper considers the problem of phase probability distribution function estimation for phase-shift-keying signals. The modulating...
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Minimum Principle for the Tikhonov Functional in the Problem of Stable Continuation of a Potential Field from a Surface
AbstractWe consider the ill-posed problem of continuation of a potential field into a cylindrical domain from a surface in three-dimensional space....
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About One Method for Numerical Solution of the Cauchy Problem for Singularly Perturbed Differential Equations
AbstractThe paper proposes a new method for numerically solving nonlinear stiff problems, based on the numerical implementation of the method of...
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Choice of Regularization Parameter in Adaptive Filtering Problems
AbstractThe paper proposes a new method for choosing a regularization parameter when solving an integral equation of convolution type in problems of...
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Iterative regularization for constrained minimization formulations of nonlinear inverse problems
In this paper we study the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton...
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Truncated SVD for Applications in Microwave Thermometry
Microwave hyperthermia is a technique used to improve the therapeutic results of traditional cancer therapies. It consists of increasing the tumor...
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Time-Adaptive Determination of Drug Efficacy in Mathematical Model of HIV Infection
The paper considers a time-adaptive finite element method for determination of drug efficacy in a parameter identification problem (PIP) for a system...
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Regularization of the Classical Optimality Conditions in Optimal Control Problems for Linear Distributed Systems of Volterra Type
AbstractRegularization of the classical optimality conditions—the Lagrange principle and the Pontryagin maximum principle—in a convex optimal control...
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Parameter estimation with the Markov Chain Monte Carlo method aided by evolutionary neural networks in a water hammer model
Fast transients in pumps and valves may induce significant variations in pressures and flow rates throughout pipelines that can even cause structural...
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Modeling the Transient Resistance of Trunk Pipeline Insulation Based on Measurements of the Magnetic Induction Vector Modulus
AbstractInterpretation of the magnetometry data of trunk pipelines in order to assess the state of their insulating coating is a relevant subtask for...
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A multidimensional analogue of the A. N. Tikhonov’s Theorem on calculating values of a function with respect to approximately given Fourier coefficients
In this paper, we study the problem of approximation to reconstruct the value of a function of several variables from the approximate values of the...
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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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Regularization Theory for Equations of the First Kind
We saw in the previous chapter that many inverse problems can be formulated as operator equations of the form...
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A Note on Quadratic Penalties for Linear Ill-Posed Problems: From Tikhonov Regularization to Mollification
The variational form of mollification fits in an extension of the generalized Tikhonov regularization. Using tools from variational analysis, we...
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Regularization by Discretization
In this chapter, we study a different approach to regularizing operator equations of the form...
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Analysis of a Regularization Algorithmfor a Linear Operator Equation Containinga Discontinuous Component of the Solution
We study a linear operator equation that does not satisfy the Hadamard well-posedness conditions. It is assumed that the solution of the equation has...