A gradient-based Newton–Krylov algorithm is presented for the aerodynamic shape optimization of singleand multi-element airfoil configurations. The flow is governed by the compressible Navier–Stokes equations in conjunction with a one-equation transport turbulence model. The preconditioned generalized minimal residual method is applied to solve the discrete-adjoint equation, which leads to a fa...

We study three wave function optimization methods based on energy minimization in a variational Monte Carlo framework: the Newton, linear, and perturbative methods. In the Newton method, the parameter variations are calculated from the energy gradient and Hessian, using a reduced variance statistical estimator for the latter. In the linear method, the parameter variations are found by diagonali...

For solving the generalized equation f (x) + F(x) 0, where f is a smooth function and F is a set-valued mapping acting between Banach spaces, we study the inexact Newton method described by ( f (xk)+ D f (xk)(xk+1 − xk)+ F(xk+1)) ∩ Rk(xk, xk+1) = ∅, where D f is the derivative of f and the sequence of mappings Rk represents the inexactness. We show how regularity properties of the mappings f + ...

We propose a randomized second-order method for optimization known as the Newton sketch: it is based on performing an approximate Newton step using a randomly projected Hessian. For self-concordant functions, we prove that the algorithm has superlinear convergence with exponentially high probability, with convergence and complexity guarantees that are independent of condition numbers and relate...

In the present paper, we consider semilocal convergence issue of two-step Newton method for solving nonlinear operator equation in Banach spaces. Under assumption that first derivative satisfies a generalized Lipschitz condition, new analysis is presented. The Q-cubic obtained by an additional condition. This also allows us to obtain three important spacial cases about results based on premises...

Abstract We discuss the generalized Newton–Cartan geometries that can serve as gravitational background fields for particles and strings. In order to enable us define affine connections are invariant under all symmetries of structure group, we describe torsionful with independent torsion tensors. A characteristic feature non-Lorentzian consider is some tensors so-called ‘intrinsic torsion’ Sett...

In this paper, an approximate formula of the fractional derivatives (Caputo sense) is derived. The proposed formula is based on the generalized Laguerre polynomials. Special attention is given to study the convergence analysis of the presented formula. The spectral Laguerre collocation method is presented for solving a class of fractional optimal control problems (FOCPs). The properties of Lagu...