A modified limited-memory BNS method for unconstrained minimization derived from the conjugate directions idea

Vlček, Jan; Lukšan, Ladislav

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.

Limited-memory variable metric methods that use quantities from the preceding iteration

Vlček, Jan, Lukšan, Ladislav

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Local Convergence Analysis for Partitioned Quasi-Newton Updates.

A. Griewank, P.L. Toint (1982)

Numerische Mathematik

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Extra multistep BFGS updates in quasi-Newton methods.

Moghrabi, Issam A.R. (2006)

International Journal of Mathematics and Mathematical Sciences

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New hybrid conjugate gradient method for nonlinear optimization with application to image restoration problems

Youcef Elhamam Hemici, Samia Khelladi, Djamel Benterki (2024)

Kybernetika

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The conjugate gradient method is one of the most effective algorithm for unconstrained nonlinear optimization problems. This is due to the fact that it does not need a lot of storage memory and its simple structure properties, which motivate us to propose a new hybrid conjugate gradient method through a convex combination of $β_{k}^{R M I L}$ and $β_{k}^{H S}$ . We compute the convex parameter $θ_{k}$ using the Newton direction. Global convergence is established through the strong Wolfe conditions. Numerical experiments...

Finite-dimensional Pullback Attractors for Non-autonomous Newton-Boussinesq Equations in Some Two-dimensional Unbounded Domains

Cung The Anh, Dang Thanh Son (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

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We study the existence and long-time behavior of weak solutions to Newton-Boussinesq equations in two-dimensional domains satisfying the Poincaré inequality. We prove the existence of a unique minimal finite-dimensional pullback $D_{σ}$ -attractor for the process associated to the problem with respect to a large class of non-autonomous forcing terms.

Quasi-Newton's method with correction.

Herceg, Dragoslav, Krejić, Nataša, Lužanin, Zorana (1996)

Novi Sad Journal of Mathematics

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Newton-type iterative methods for nonlinear ill-posed Hammerstein-type equations

Monnanda Erappa Shobha, Ioannis K. Argyros, Santhosh George (2014)

Applicationes Mathematicae

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We use a combination of modified Newton method and Tikhonov regularization to obtain a stable approximate solution for nonlinear ill-posed Hammerstein-type operator equations KF(x) = y. It is assumed that the available data is $y^{δ}$ with $| | y - y^{δ} | | \leq δ$ , K: Z → Y is a bounded linear operator and F: X → Z is a nonlinear operator where X,Y,Z are Hilbert spaces. Two cases of F are considered: where $F^{'} {(x ₀)}^{- 1}$ exists (F’(x₀) is the Fréchet derivative of F at an initial guess x₀) and where F is a monotone operator....