Abstract In this paper, we present a new nonsmooth Newton-type algorithm for solving the generalized complementarity problem based on its reformulation as system of nonlinear equations using one-parametric family functions. We demonstrate, under suitable hypotheses, that converges locally and q -quadratically. addition, show numerical experiments allow us to see good performance proposed algori...

An efficient multi-block Newton–Krylov algorithm using the compressible Navier–Stokes equations is presented for the analysis and design of high-lift airfoil configurations. The preconditioned generalized minimum residual (GMRES) method is applied to solve the discreteadjoint equation, leading to a fast computation of accurate objective function gradients. Furthermore, the GMRES method is used ...

We introduce in the present paper a Gauss–Newton-type method for solving generalized equations defined by sums of differentiable mappings and set-valued mappings in Banach spaces. Semi-local convergence and local convergence of the Gauss–Newton-type method are analyzed.

Abstract In a recent paper, conformable fractional Newton-type method was proposed for solving nonlinear equations. This involves lower computational cost compared to other iterative methods. Indeed, the theoretical order of convergence is held in practice, and it presents better numerical behaviour than methods formerly proposed, even classical Newton-Raphson method. this work, we design gener...

In the present paper, we consider generalized equation $0\in f(x)+g(x)+\mathcal F(x)$, where $f:\mathcal X\to \mathcal Y$ is Fr\'{e}chet differentiable on a neighborhood $\Omega$ of point $\bar{x}$ in $\mathcal X$, $g:\mathcal at and linear as well F$ set-valued mapping with closed graph acting between two Banach spaces X$ Y$. We study above help extended Newton-type method, introduced [ M. Z. ...

In this paper, we study the problem of minimizing the ratio of two quadratic functions subject to a quadratic constraint. First we introduce a parametric equivalent of the problem. Then a bisection and a generalized Newton-based method algorithms are presented to solve it. In order to solve the quadratically constrained quadratic minimization problem within both algorithms, a semidefinite optim...

This paper concerns developing a numerical method of the Newton type to solve systems of nonlinear equations described by nonsmooth continuous functions. We propose and justify a new generalized Newton algorithm based on graphical derivatives, which have never been used to derive a Newton-type method for solving nonsmooth equations. Based on advanced techniques of variational analysis and gener...

Multigrid algorithms are developed for systems arising from high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations on unstructured meshes. The algorithms are based on coupling both pand h-multigrid (ph-multigrid) methods which are used in non-linear or linear forms, and either directly as solvers or as preconditioners to a Newton-Krylov method. The perform...

We consider a regularization method for nonlinear complementarity problems with F being a P0-function which replaces the original problem with a sequence of the regularized complementarity problems. In this paper, this sequence of regularized complementarity problems are solved approximately by applying the generalized Newton method for an equivalent augmented system of equations, constructed b...