and Applied Analysis 3 Additionally, we assume that there exist positive constants γ and γ such that 0 < γ ≤ 󵄩󵄩󵄩gk 󵄩󵄩󵄩 ≤ γ, ∀k ≥ 1, (21) then we have the following result. Theorem2. Consider the method (2), (8) and (12), where d k is a descent direction. If (21) holds, there exist positive constants ξ 1 , ξ 2 , and ξ 3 such that relations

Correcting an inconsistent set of linear inequalities by minimal changes in problem data is a well studied problem and up to now several algorithms have been developed to do this task. In this paper, we consider doing the minimal correction using the l2 norm by changing just the right hand vector. A new formulation of the problem is introduced and its relation with the normal solution of the al...

In this paper, the Newton-conjugate-gradient methods are developed for solitary wave computations. These methods are based on Newton iterations, coupled with conjugategradient iterations to solve the resulting linear Newton-correction equation. When the linearization operator is self-adjoint, the preconditioned conjugate-gradient method is proposed to solve this linear equation. If the lineariz...

This study concerns the fast and accurate solution of the line radiation transfer problem, under non-LTE conditions. We propose and evaluate an alternative iterative scheme to the classical ALI-Jacobi method, and to the more recently proposed Gauss-Seidel and Successive Over-Relaxation (GS/SOR) schemes. Our study is indeed based on the application of a preconditioned bi-conjugate gradient metho...

Using an extension of some previously proposed modified secant equations in the Dai–Liao approach, a modified nonlinear conjugate gradient method is proposed. As interesting features, the method employs the objective function values in addition to the gradient information and satisfies the sufficient descent property with proper choices for its parameter. Global convergence of the method is est...

Numerical identification of diffusion parameters in a nonlinear convection–diffusion equation is studied. This partial differential equation arises as the saturation equation in the fractional flow formulation of the two–phase porous media flow equations. The forward problem is discretized with the finite difference method, and the identification problem is formulated as a constrained minimizat...

1. This note summarizes a paper [4] to appear in full elsewhere. It presents an algorithm for the minimization of a general (not necessarily differentiable) convex function. Its central idea is the construction of descent directions as projections of the origin onto the convex hull of previously calculated subgradients as long as satisfactory progress can be made. Using projection to obtain a d...