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- research-articleSeptember 2024
Reconstruction of a Singular Source in a Fractional Subdiffusion Problem from a Single Point Measurement
Applied Mathematics and Optimization (APMO), Volume 90, Issue 2https://doi.org/10.1007/s00245-024-10185-8AbstractIn this paper, we reconstruct a singular time dependent source function of a fractional subdiffusion problem using observational data obtained from a single point of the boundary and inside of the domain. Specifically, the singular function under ...
- research-articleJuly 2024
Levenberg-Marquardt method with singular scaling and applications
Applied Mathematics and Computation (APMC), Volume 474, Issue Chttps://doi.org/10.1016/j.amc.2024.128688AbstractInspired by certain regularization techniques for linear inverse problems, in this work we investigate the convergence properties of the Levenberg-Marquardt method using singular scaling matrices. Under a completeness condition, we show that the ...
Highlights- A variation of the Levenberg-Marquardt method that uses singular scaling matrices is proposed.
- Under mild conditions, local quadratic convergence is established under an error bound assumption.
- A globalization strategy produces ...
- research-articleJuly 2024
Computing the Minimum-Time Interception of a Moving Target
Journal of Optimization Theory and Applications (JOPT), Volume 202, Issue 2Pages 975–995https://doi.org/10.1007/s10957-024-02487-2AbstractIn this study, we propose an algorithmic framework for solving a class of optimal control problems. This class is associated with the minimum-time interception of moving target problems, where a plant with a given state equation must approach a ...
- research-articleApril 2024
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- research-articleApril 2024
Global convergence of a BFGS-type algorithm for nonconvex multiobjective optimization problems
Computational Optimization and Applications (COOP), Volume 88, Issue 3Pages 719–757https://doi.org/10.1007/s10589-024-00571-xAbstractWe propose a modified BFGS algorithm for multiobjective optimization problems with global convergence, even in the absence of convexity assumptions on the objective functions. Furthermore, we establish a local superlinear rate of convergence of ...
- research-articleApril 2024
On a unified convergence analysis for Newton-type methods solving generalized equations with the Aubin property
AbstractA plethora of applications from diverse disciplines reduce to solving generalized equations involving Banach space valued operators. These equations are solved mostly iteratively, when a sequence is generated approximating a solution provided ...
- research-articleMarch 2024
Secant-inexact projection algorithms for solving a new class of constrained mixed generalized equations problems
Journal of Computational and Applied Mathematics (JCAM), Volume 440, Issue Chttps://doi.org/10.1016/j.cam.2023.115638AbstractIn this paper, a new version of a secant-type method for solving constrained mixed generalized equations is addressed. The method is a combination of the secant method applied to generalized equations with the conditional gradient method. We use ...
- research-articleFebruary 2024
Convergence of the Gauss-Newton method for convex composite optimization problems under majorant condition on Riemannian manifolds
AbstractIn this paper, we consider convex composite optimization problems on Riemannian manifolds, and discuss the semi-local convergence of the Gauss-Newton method with quasi-regular initial point and under the majorant condition. As special cases, we ...
Highlights- Study of convex composite optimization problems on Riemannian manifolds.
- Convergence of the Gauss-Newton method under the majorant condition.
- Special cases are studied under (i) Lipschitz-type condition, (ii) γ-condition.
- research-articleJanuary 2024
An inexact semismooth Newton method with application to adaptive randomized sketching for dynamic optimization
Finite Elements in Analysis and Design (FEAD), Volume 228, Issue Chttps://doi.org/10.1016/j.finel.2023.104052AbstractIn many applications, one can only access the inexact gradients and inexact hessian times vector products. Thus it is essential to consider algorithms that can handle such inexact quantities with a guaranteed convergence to solution. An inexact ...
Highlights- An inexact adaptive and provably convergent semismooth Newton method is introduced.
- Rigorous convergence of this method in function spaces is established.
- The source of efficiency and inexactness is the randomized matrix sketching.
- research-articleDecember 2023
A Bregman–Kaczmarz method for nonlinear systems of equations
Computational Optimization and Applications (COOP), Volume 87, Issue 3Pages 1059–1098https://doi.org/10.1007/s10589-023-00541-9AbstractWe propose a new randomized method for solving systems of nonlinear equations, which can find sparse solutions or solutions under certain simple constraints. The scheme only takes gradients of component functions and uses Bregman projections onto ...
- research-articleOctober 2023
Preconditioning of discrete state- and control-constrained optimal control convection-diffusion problems
Calcolo: a quarterly on numerical analysis and theory of computation (CALCOLO), Volume 60, Issue 4https://doi.org/10.1007/s10092-023-00542-4AbstractWe consider the iterative solution of algebraic systems, arising in optimal control problems constrained by a partial differential equation with additional box constraints on the state and the control variables, and sparsity imposed on the ...
- research-articleOctober 2023
An Efficient Implementation of the Gauss–Newton Method Via Generalized Krylov Subspaces
Journal of Scientific Computing (JSCI), Volume 97, Issue 2https://doi.org/10.1007/s10915-023-02360-wAbstractThe solution of nonlinear inverse problems is a challenging task in numerical analysis. In most cases, this kind of problems is solved by iterative procedures that, at each iteration, linearize the problem in a neighborhood of the currently ...
- research-articleAugust 2023
Inexact proximal Newton methods in Hilbert spaces
Computational Optimization and Applications (COOP), Volume 87, Issue 1Pages 1–37https://doi.org/10.1007/s10589-023-00515-xAbstractWe consider proximal Newton methods with an inexact computation of update steps. To this end, we introduce two inexactness criteria which characterize sufficient accuracy of these update step and with the aid of these investigate global ...
- research-articleJuly 2023
Local and Semi-local convergence for Chebyshev two point like methods with applications in different fields
Journal of Computational and Applied Mathematics (JCAM), Volume 426, Issue Chttps://doi.org/10.1016/j.cam.2023.115072AbstractThe convergence is developed for a large class of Chebyshev-two point-like methods for solving Banach space valued equations. Both the local as well as the semi-local convergence is provided for these methods under general conditions ...
- research-articleJune 2023
Inexact free derivative quasi-Newton method for large-scale nonlinear system of equations
Numerical Algorithms (SPNA), Volume 94, Issue 3Pages 1103–1123https://doi.org/10.1007/s11075-023-01529-6AbstractIn this work, we propose a free derivative quasi-Newton method for solving large-scale nonlinear systems of equation. We introduce a two-stage linear search direction and develop its global convergence theory. Besides, we prove that the method ...