Displaying similar documents to “A modified limited-memory BNS method for unconstrained minimization derived from the conjugate directions idea”

New quasi-Newton method for solving systems of nonlinear equations

Ladislav Lukšan, Jan Vlček (2017)

Applications of Mathematics

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We propose a new Broyden method for solving systems of nonlinear equations, which uses the first derivatives, but is more efficient than the Newton method (measured by the computational time) for larger dense systems. The new method updates QR or LU decompositions of nonsymmetric approximations of the Jacobian matrix, so it requires O ( n 2 ) arithmetic operations per iteration in contrast with the Newton method, which requires O ( n 3 ) operations per iteration. Computational experiments confirm the...

Inexact Newton-type method for solving large-scale absolute value equation A x - | x | = b

Jingyong Tang (2024)

Applications of Mathematics

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Newton-type methods have been successfully applied to solve the absolute value equation A x - | x | = b (denoted by AVE). This class of methods usually solves a system of linear equations exactly in each iteration. However, for large-scale AVEs, solving the corresponding system exactly may be expensive. In this paper, we propose an inexact Newton-type method for solving the AVE. In each iteration, the proposed method solves the corresponding system only approximately. Moreover, it adopts a new line...

A new diagonal quasi-Newton algorithm for unconstrained optimization problems

Mahsa Nosrati, Keyvan Amini (2024)

Applications of Mathematics

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We present a new diagonal quasi-Newton method for solving unconstrained optimization problems based on the weak secant equation. To control the diagonal elements, the new method uses new criteria to generate the Hessian approximation. We establish the global convergence of the proposed method with the Armijo line search. Numerical results on a collection of standard test problems demonstrate the superiority of the proposed method over several existing diagonal methods.