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...

This paper deals with an algorithm which incorporates the interior point method into the Dantzig-Wolfe decomposition technique for solving large-scale linear programming problems. At each iteration, the algorithm performs one step of Newton's method to solve a subproblem, obtaining an approximate solution, which is then used to compute an approximate Newton direction to nd a new vector of the L...

This paper introduces new contrast functions for blind separation of sources with different time-frequency signatures. Two contrast functions based on the Kullback-Leibler and Jensen-Rényi divergences in the time-frequency (T-F) plane are introduced. Two iterative algorithms are proposed for the proposed contrasts optimization and source separation. One algorithm consists of spatial whitening a...

Abstract. In competitive electric reserve markets, the suppliers face the optimal allocation problem of their reserve capacities in order to purse their profit maximizing. Under this background, we develop a capacity allocation model as nonlinear programming. Nonlinear complementarity method is utilized to search for the optimal solution. And smoothing technique is applied to get a system of sm...

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...

In this paper, synchronization of memristor-based neural networks (MNNs) with time-varying delays is investigated. By employing the Newton–Leibniz formulation and inequality technique, the controller with state or output coupling is designed to obtain global exponential synchronization of MNNs. The obtained delay-dependent conditions can be checked easily and they also enrich and improve the re...

In this paper, the direct method is utilized for solving second order two-point boundary value problem of Neumann type. The method will obtain the solution of the second order boundary value problem directly without reducing it to to first order equations. The method will be implemented using variable step size via shooting technique adapted with the Newton method. Numerical results are given t...

Conventional methods of supervised learning are inevitably faced with the problem of local minima; evidence is presented that conjugate gradient and quasi-Newton techniques are particularly susceptible to being trapped in sub-optimal solutions. A new classical technique is presented which by the use of a homotopy on the range of the target outputs allows supervised learning methods to find a gl...

A new approach to the problem of minimizing L2sensitivity subject to L2-norm scaling constraints for two-dimensional (2-D) state-space digital filters is proposed. Using linear-algebraic techniques, the problem at hand is converted into an unconstrained optimization problem, and the unconstrained problem obtained is then solved by applying an efficient quasi-Newton algorithm. Computer simulatio...