Global Topological Linearization with Unbounded Nonlinear Term

In 1960s, Hartman and Grobman pointed out that if all eigenvalues of a matrix A have no zero real part and f(x) is small Lipchitzian, then x′=Ax+f(x) can be locally linearized on a neighborhood of the origin. Later, the above result was generalized to global under the condition that f(x) is a bounded function. In this paper, we delete the condition that f(x) is a bounded function, and prove that if f(x) has suitable structure, then x′=Ax+f(x) can be linearized.

GLOBAL LINEARIZATION OF DIFFERENTIAL EQUATIONS WITH SPECIAL STRUCTURES

This paper introduces the global linearization of the differential equations with special structures.The function in the differential equation is unbounded.We prove that the differential equation with unbounded function can be topologically linearlized if it has a special structure.

Generalized LMI-based approach to global asymptotic stability of cellular neural networks with delay

A global asymptotic stability problem of cellular neural networks with delay is investigated. A new stability condition is presented based on the Lyapunov-Krasovskii method, which is dependent on the amount of delay. A result is given in the form of a linear matrix inequality, and the admitted upper bound of the delay can be easily obtained. The time delay dependent and independent results can be obtained, which include some previously published results. A numerical example is given to show the effectiveness of the main results.

GLOBAL LINEAR AND QUADRATIC ONE-STEP SMOOTHING NEWTON METHOD FOR VERTICAL LINEAR COMPLEMENTARITY PROBLEMS

A one_step smoothing Newton method is proposed for solving the vertical linear complementarity problem based on the so_called aggregation function. The proposed algorithm has the following good features: (ⅰ) It solves only one linear system of equations and does only one line search at each iteration; (ⅱ) It is well_defined for the vertical linear complementarity problem with vertical block P 0 matrix and any accumulation point of iteration sequence is its solution.Moreover, the iteration sequence is bounded for the vertical linear complementarity problem with vertical block P 0+R 0 matrix; (ⅲ) It has both global linear and local quadratic convergence without strict complementarity. Many existing smoothing Newton methods do not have the property (ⅲ).

Global stability of interval recurrent neural networks

The robust global exponential stability of a class of interval recurrent neural networks（RNNs） is studied,and a new robust stability criterion is obtained in the form of linear matrix inequality.The problem of robust stability of interval RNNs is transformed into a problem of solving a class of linear matrix inequalities.Thus,the robust stability of interval RNNs can be analyzed by directly using the linear matrix inequalities（LMI） toolbox of MATLAB.Numerical example is given to show the effectiveness of the obtained results.

LINEAR INDEPENDENCE OF THE INTEGER TRANS-LATES OF COMPACTLY SUPPORTED DISTRIBU-TIONS AND REFINABLE VECTORS

In this paper,the global and local linear independence of any compactly supported distributions by using time domain spaces,and of refinable vectors by invariant linear spaces are investigated.

Stability analysis of extended discrete-time BAMneural networks based on LMI approach

We propose a new approach for analyzing the global asymptotic stability of the extended discrete-time bidirectional associative memory （BAM） neural networks. By using the Euler rule, we discretize the continuous-time BAM neural networks as the extended discrete-time BAM neural networks with non-threshold activation functions. Here we present some conditions under which the neural networks have unique equilibrium points. To judge the global asymptotic stability of the equilibrium points, we introduce a new neural network model - standard neural network model （SNNM）. For the SNNMs, we derive the sufficient conditions for the global asymptotic stability of the equilibrium points, which are formulated as some linear matrix inequalities （LMIs）. We transform the discrete-time BAM into the SNNM and apply the general result about the SNNM to the determination of global asymptotic stability of the discrete-time BAM. The approach proposed extends the known stability results, has lower conservativeness, can be verified easily, and can also be applied to other forms of recurrent neural networks.

A CFD-Aided Galerkin Method for Global Linear Instability Analysis

Global linear instability analysis is a powerful tool for the complex flow diagnosis.However,the methods used in the past would generally suffer from some dis-advantages,either the excessive computational resources for the low-order methods or the tedious mathematical derivations for the high-order methods.The present work proposed a CFD-aided Galerkin methodology which combines the merits from both the low-order and high-order methods,where the expansion on proper basis func-tions is preserved to ensure a small matrix size,while the differentials,incompressibility constraints and boundary conditions are realized by applying the low-order linearized Navier-Stokes equation solvers on the basis functions on a fine grid.Several test cases have shown that the new method can get satisfactory results for one-dimensional,two-dimensional and three-dimensional flow problems and also for the problems with complex geometries and boundary conditions.

FINDING THE STRICTLY LOCAL AND ε-GLOBAL MINIMIZERS OF CONCAVE MINIMIZATION WITH LINEAR CONSTRAINTS

This paper considers the concave minimization problem with linear constrailits,proposes a technique which may avoid the unsuitable Karush-Kuhn-Tucker poiats,then combines this technique with nank-Wolfe method and simplex method to form a pivoting method which can determine a strictly local minimizer of the problem in a finite number of iterations. Basing on strictly local minimizers, a new cutting plane method is proposed. Under some mild conditions, the new cutting plane method is proved to be finitely terminated at an θ-global minimizer of the problem.

Convergence of a Non-interior Continuation Algorithm for the Monotone SCCP

It is well known that the symmetric cone complementarity problem（SCCP） is a broad class of optimization problems which contains many optimization problems as special cases.Based on a general smoothing function,we propose in this paper a non-interior continuation algorithm for solving the monotone SCCP.The proposed algorithm solves at most one system of linear equations at each iteration.By using the theory of Euclidean Jordan algebras,we show that the algorithm is globally linearly and locally quadratically convergent under suitable assumptions.

An Improved Feasible QP-free Algorithm for Inequality Constrained Optimization

In this paper, an improved feasible QP-free method is proposed to solve nonlinear inequality constrained optimization problems. Here, a new modified method is presented to obtain the revised feasible descent direction. In view of the computational cost, the most attractive feature of the new algorithm is that only one system of linear equations is required to obtain the revised feasible descent direction. Thereby, per single iteration, it is only necessary to solve three systems of linear equations with the same coefficient matrix. In particular, without the positive definiteness assumption on the Hessian estimate, the proposed algorithm is still global convergence. Under some suitable conditions, the superlinear convergence rate is obtained.