In this paper, we present an inexact full Newton optimization method for the full waveform inversion algorithm in the frequency domain which utilizes simultaneous sources based upon the phase encoding technique. Tests show that the full Newton minimization method achieves a high convergence rate and a reasonably accurate reconstruction of the model parameters. Taking advantage of a direct solve...

We investigate the efficiency of multi-step Newton method (the classical Newton method in which the first derivative is re-evaluated periodically after m steps) for solving nonlinear equations, F(x) = 0, F : D ⊆ Rn → Rn. We highlight the following property of multi-step Newton method with respect to some other Newton-type method: for a given n, there exist thresholds of m, that is an interval (...

Inexact Newton methods are constructed by combining Newton’s method with another iterative method that is used to solve the Newton equations inexactly. In this paper, we establish two semilocal convergence theorems for the inexact Newton methods. When these two theorems are specified to Newton’s method, we obtain a different Newton-Kantorovich theorem about Newton’s method. When the iterative m...

Inexact Newton methods are constructed by combining Newton’s method with another iterative method that is used to solve the Newton equations inexactly. In this paper, we establish two semilocal convergence theorems for the inexact Newton methods. When these two theorems are specified to Newton’s method, we obtain a different Newton-Kantorovich theorem about Newton’s method. When the iterative m...

We consider an interior point method in function space for PDE constrained optimal control problems with state constraints. Our emphasis is on the construction and analysis of an algorithm that integrates a Newton path-following method with adaptive grid refinement. This is done in the framework of inexact Newton methods in function space, where the discretization error of each Newton step is c...

We present a modified version of the infeasible-interior- We present a modified version of the infeasible-interior-point algorithm for monotone linear complementary problems introduced by Mansouri et al. (Nonlinear Anal. Real World Appl. 12(2011) 545--561). Each main step of the algorithm consists of a feasibility step and several centering steps. We use a different feasibility step, which tar...

Recently, Roos proposed a full-Newton step infeasible interiorpoint method (IIPM) for solving linear optimization (LO) problems. Later on, more variants of this algorithm were published. However, each main step of these methods is composed of one feasibility step and several centering steps. The purpose of this paper is to prove that by using a new search direction it is enough to take only one...