A Three-Step Iterative Method for Solving Absolute Value Equations

In this paper, we transform the problem of solving the absolute value equations (AVEs) Ax−x=b with singular values of A greater than 1 into the problem of finding the root of the system of nonlinear equation and propose a three-step algorithm for solving the system of nonlinear equation. The proposed method has the global linear convergence and the local quadratic convergence. Numerical examples show that this algorithm has high accuracy and fast convergence speed for solving the system of nonlinear equations.

Sparse Spike Deconvolution of Seismic Data Using Trust-Region Based SQP Algorithm

A new deconvolution algorithm for retrieving a sparse reflectivity series from noisy seismic traces is proposed. The problem is formulated as a constrained minimization, taking the approximation zero norm of reflectivity as the objective function. The resulting minimization is solved efficiently by the trust-region based sequential quadratic programming (SQP) method, which provides global convergence and local quadratic convergence rates under suitable assumptions. The null space decomposition method and the de-biasing method are employed to reduce computational complexity and further improve the calculation accuracy. Synthetic simulations indicate that the spikes on the reflectivity, both their positions and amplitudes, are recovered effectively by the proposed approach.

A New Jacobian-Like Method for the Polyhedral Cone-Constrained Eigenvalue Problem

The eigenvalue problem over a polyhedral cone is studied in this paper. Based on the F-B NCP function, we reformulate this problem as a system of equations and propose a Jacobian-like method. The global convergence and local quadratic convergence of the proposed method are established under suitable assumptions. Preliminary numerical experiments for a special polyhedral cone are reported in this paper to show the validity of the proposed method.

A New Searching Direction for Linear Complementarity Problems

In this paper, we investigate the properties of a simple function. As an application, we present a full-step interior-point algorithm for linear complementarity problem. The algorithm uses the simple function to determine the searching direction and define the neighborhood of central path. The full-step used in the algorithm has local quadratic convergence property according to the proximity function which is also constructed by this simple function. We derive the iteration complexity for the algorithm and obtain the best-known iteration bounds for linear complementarity problem.