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Relaxed-based matrix splitting methods for solving absolute value equations
In this paper, we investigate the iterative methods for solving the absolute value equations (AVEs). Using matrix splitting and the relaxed...
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Relaxed-inertial derivative-free algorithm for systems of nonlinear pseudo-monotone equations
Solving systems of nonlinear equations has evolved into an active research field, with numerous iterative methods being proposed. Notably, iterative...
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A Relaxed Interior Point Method for Low-Rank Semidefinite Programming Problems with Applications to Matrix Completion
A new relaxed variant of interior point method for low-rank semidefinite programming problems is proposed in this paper. The method is a step outside...
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Randomized Kaczmarz Method for Single Particle X-Ray Image Phase Retrieval
In this chapter, we investigate phase retrieval algorithm for the single-particle X-ray imaging data. We present a variance-reduced randomized...
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A nonsmooth primal-dual method with interwoven PDE constraint solver
We introduce an efficient first-order primal-dual method for the solution of nonsmooth PDE-constrained optimization problems. We achieve this...
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On Global and Monotone Convergence of the Preconditioned Newton’s Method for Some Mildly Nonlinear Systems
Let β be a diagonal map** from RN to itself and let A be an N X N real matrix.
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An Adaptive Orthogonal Basis Method for Computing Multiple Solutions of Differential Equations with Polynomial Nonlinearities
This paper presents an innovative approach, the Adaptive Orthogonal Basis Method, tailored for computing multiple solutions to differential equations...
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An Efficient Spectral Trust-Region Deflation Method for Multiple Solutions
It is quite common that a nonlinear partial differential equation (PDE) admits multiple distinct solutions and each solution may carry a unique...
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A Semi-Implicit Numerical Method for Differentially Rotating Compressible Flows
AbstractIn astrophysical fluid dynamics, some types of flows, like e.g., magnetorotational supernova explosions, deal with a highly variable Mach...
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The Levenberg–Marquardt method: an overview of modern convergence theories and more
The Levenberg–Marquardt method is a fundamental regularization technique for the Newton method applied to nonlinear equations, possibly constrained,...
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Randomized Kaczmarz Method for Single-Particle X-Ray Image Phase Retrieval
In this chapter, we investigate phase retrieval algorithm for the single-particle X-ray imaging data. We present a variance-reduced randomized...
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Limited Memory BFGS Method for Least Squares Semidefinite Programming with Banded Structure
This work is intended to solve the least squares semidefinite program with a banded structure. A limited memory BFGS method is presented to solve...
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On finite termination of the generalized Newton method for solving absolute value equations
Motivated by the framework constructed by Brugnano and Casulli (SIAM J. Sci. Comput. 30: 463–472, 2008), we analyze the finite termination property...
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Numerical Methods of Optimization
The numerical methods of optimization start with optimizing functions of one variable, bisection, Fibonacci, and Newton. Then, functions of several...
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An inertial Fletcher–Reeves-type conjugate gradient projection-based method and its spectral extension for constrained nonlinear equations
In this paper, we initially enhance the Fletcher–Reeves (FR) conjugate parameter through a shrinkage multiplier, leading to a derivative-free...
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Enhancing the Convergence of the Multigrid-Reduction-in-Time Method for the Euler and Navier–Stokes Equations
Excessive spatial parallelization can introduce a performance bottleneck due to the communication overhead. While time-parallel method...
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A semismooth Newton based augmented Lagrangian method for nonsmooth optimization on matrix manifolds
This paper is devoted to studying an augmented Lagrangian method for solving a class of manifold optimization problems, which have nonsmooth...
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An Improved Coupled Level Set and Continuous Moment-of-Fluid Method for Simulating Multiphase Flows with Phase Change
An improved algorithm for computing multiphase flows is presented in which the multimaterial Moment-of-Fluid (MOF) algorithm for multiphase flows,...
