Least-change quasi-Newton updates for equality-constrained optimization

This paper investigates quasi-Newton updates for equality-constrained optimization. Using a least-change argument we derive a class of rank-3 updates to approximations of the one-sided projection of the Hessian of the Lagrangian which keeps the appropriate part symmetric (and possibly positive definite). By imposing the usual assumptions we are able to prove 1-step superlinear convergence for one of these updates. Encouraging numerical results and comparisons with other previously analyzed updates are presented. Received: May 3, 1999 / Accepted: January 28, 2000?Published online March 15, 2000     

Limited memory quasi-newton method for large-scale linearly equality-constrained minimization

1. IntroductionConsider the following linearly constrained nonlinear programming problemwhere x e R", A E Rmxn and f E C2. We are interested in the case when n and m arelarge and when the Hessian matrix of f is difficult to compute or is dense. It is ajssumed thatA is a matrix of full row rank and that the level set S(xo) = {x: f(x) 5 f(xo), Ax ~ b} isnonempty and compact.In the past few years j there were two kinds of methods for solving the large-scaleproblem (1.1). FOr the one kind, pr…     

Asymptotic stability of differential systems of neutral type

We offer sufficient conditions for the asymptotic stability of the equilibrium point of linear neutral differential systems. An application of our results to a family of artificial neural networks of neutral type is also illustrated.     

On the Hyers-Ulam stability of the linear differential equation

We obtain some results on generalized Hyers-Ulam stability of the linear differential equation in a Banach space. As a consequence we improve some known estimates of the difference between the perturbed and the exact solutions.     

On the stability of the linear differential equation of higher order with constant coefficients

We obtain a result on stability of the linear differential equation of higher order with constant coefficients in Aoki-Rassias sense. As a consequence we obtain the Hyers-Ulam stability of the above mentioned equation. A connection with dynamical sytems perturbation is established.     

Asymptotic behavior of a differential equation with distributed delays

In this paper, sufficient conditions are established for the asymptotical behavior of solutions of the delay differential equation

x^′(t)=F(t,xt)+G(t,xt)     

Variable structure control for a class of nonlinear systems with mismatched uncertainties

A scheme to stabilize nonlinear time-varying systems with both matched and mismatched uncertainties is proposed in this paper by switching between two control laws: a first-order sliding-mode control and a second-order sliding-mode control. Based on this idea, a variable structure control algorithm is designed for a class of second-order systems. The closed-loop system is globally or locally asymptotically stable. It has been proven that the stability region has relation with the order of the boundary function and the region can be obtained by solving an inequality. The uncertainty considered in this work is also more general than those in the existing works.     

A novel hybrid differential evolution and particle swarm optimization algorithm for unconstrained optimization

An algorithm called DE-PSO is proposed which incorporates concepts from DE and PSO, updating particles not only by DE operators but also by mechanisms of PSO. The proposed algorithm is tested on several benchmark functions. Numerical comparisons with different hybrid meta-heuristics demonstrate its effectiveness and efficiency.     

A note on the Riccati differential equation

In this note, we obtain some results for the Riccati differential equations u′=A(z)+u² with nonentire meromorphic functions A(z). Some examples are given to illustrate our some results are sharp.     

A differential equation approach to nonlinear programming

A new method is presented for finding a local optimum of the equality constrained nonlinear programming problem. A nonlinear autonomous system is introduced as the base of the theory instead of usual approaches. The relation between critical points and local optima of the original optimization problem is proved. Asymptotic stability of the critical points is also proved. A numerical algorithm which is capable of finding local optima systematically at the quadratic rate of convergence is developed from a detailed analysis of the nature of trajectories and critical points. Some numerical results are given to show the efficiency of the method.     

Oscillation of neutral differential equation with positive and negative coefficients

In this paper, we provide oscillation properties of every solution of the neutral differential equation with positive and negative coefficients

[x(t)−R(t)x(t−r)^]′+P(t)x(t−τ)−Q(t)x(t−σ)=0,     

A dynamic clustering based differential evolution algorithm for global optimization

A dynamic clustering based differential evolution algorithm (CDE) for global optimization is proposed to improve the performance of the differential evolution (DE) algorithm. With population evolution, CDE algorithm gradually changes from exploring promising areas at the early stages to exploiting solution with high precision at the later stages. Experiments on 28 benchmark problems, including 13 high dimensional functions, show that the new method is able to find near optimal solutions efficiently. Compared with other existing algorithms, CDE improves solution accuracy with less computational effort.     

解线性等式约束优化问题的模式搜索过滤集方法

提出一个解线性等式约束无导数优化的模式搜索过滤集算法,该算法将过滤集技术嵌入无导数优化算法中以改善算法的效率. 建立了新算法的总体收敛性, 初步的数值试验结果表明新算法是有效的.     

A gentle introduction to the differential equation method and dynamic concentration

We discuss the differential equation method for establishing dynamic concentration of discrete random processes. We present several relatively simple examples of it and aim to make the method understandable to the unfamiliar reader who has some basic knowledge on probabilistic methods, random graphs and differential equations.     

On the solution of a class of the reduced wave equation and the Riccati differential equation

In this paper we present an “iteration” technique for a class of differential equation having the form z^″=λz, where λ is a function in C^∞. We show that we can construct not only the general solution of the reduced wave equation but also the general solution of the Riccati differential equation by using this iteration technique if the given function λ is satisfies the condition

     

Asymptotic behavior of solutions for nonlinear delay differential equation with impulses

This paper studies the asymptotic behavior of solutions of the nonlinear delay differential equation with impulses

     

On the Isaacs equation of differential games of fixed duration

The conditions under which the value function of fixed-duration differential games satisfies the Isaacs equation are relaxed.The author thanks Professor L. D. Berkovitz for posing the problem.