Interative approximation of fixed points for almost asymptotically nonexpansive type mappings in Banach spaces

IntroductionThroughoutthispaperweassumethatEisarealBanachspace ,E isthedualspaceofE ,DisanonemptysubsetofEandJ:E →2 E isthenormalizeddualitymappingdefinedbyJ(x) =f∈E :〈x ,f〉=‖x‖·‖f‖,‖f‖=‖x‖,　　 x∈E .　　Definition 1　LetT :D →Dbeamapping .1 )Tissaidtobeasymptoticallynonexpansive[1],ifthereexistsasequence kn [1 ,∞)withlimn→∞kn =1suchthat　　　　　‖Tnx-Tny‖≤kn‖x-y‖forall　　x ,y∈D ,n≥0 ;(1 )　　2 )Tissaidtobeofasymptoticallynonexpansivetype[2 ],if　　　　　lims…     

Iterative algorithms for finding approximate solutions of completely generalized strongly nonlinear quasivariational inequalities

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Approximate solution to a class of multivalued nonlinear mixed variational inclusions

IntroductionIn recent years,the theory of variational inclusion has appeared as an elegant andfascinating branch of pure and applied mathematics.This theory provides us with a convenientmathematical apparatus for uniformly studying a wide range of problem…     

Generalized H-η-accretive operators in Banach spaces with application to variational inclusions

In this paper, a new notion of a generalized H-η-accretive operator is introduced and studied, which provides a unifying framework for the generalized m-accretive operator and the H-η-monotone operator in Banach spaces. A resolvent operator associated with the generalized H-η-accretive operator is defined, and its Lipschitz continuity is shown. As an application, the solvability for a class of variational inclusions involving the generalized H-η-accretive operators in Banach spaces is considered. By using the technique of the resolvent mapping, an iterative algorithm for solving the variational inclusion in Banach spaces is constructed. Under some suitable conditions, it is proven that the solution for the variational inclusion and the convergence of the iterative sequence generated by the algorithm exist.     

结构性软土弹塑性模型的隐式算法实现

对于考虑软土结构性的高度非线性弹塑性本构模型,在采用Newton-CPPM隐式算法对模型进行数值实现的过程中容易出现Jacobian矩阵奇异和不收敛问题。为此,本文提出了两种改进隐式算法。考虑到Newton-CPPM隐式算法是局部收敛性算法,因此引入大范围收敛的同伦延拓算法对Newton-CPPM算法的迭代初值进行改进,形成了同伦-Newton-CPPM算法。考虑到Newton-CPPM隐式算法单个迭代步的计算量过大,因此借鉴显式算法的思想提出一种两阶段迭代算法,第一阶段先求出一致性参数,第二阶段采用类似于显示算法的方法进行回代得出状态变量的值。然后,以考虑软土结构性的SANICLAY模型为例,从弹塑性本构模型的组成和算法的特点两个角度分析了引起Jacobian矩阵奇异和不收敛问题的原因,并且在单单元计算的基础上,对全显式算法、传统隐式算法和两种改进隐式算法在计算收敛性、计算精度和计算效率方面进行了对比。最后,将同伦-Newton-CPPM算法和传统隐式算法用于地基承载力多单元计算中,结果表明该算法能够有效地解决Jacobian矩阵奇异和不收敛问题。      

Stability of elastic and viscoelastic systems under a random perturbations of their parameters

Summary The present paper is concerned with the investigation of the almost sure stability of elastic and viscoelastic systems, when their parameters assume a random wide-band stationary process. The parameters are parametric loads, characteristics of external damping and material viscosity. With the help of Liapunov's direct method, the sufficient condition of the almost sure asymptotic stability for distributed parameter systems with respect to perturbations of initial conditions of an arbitrary form is obtained. It is shown that, in some cases, this condition coincides with a similar condition derived from the assumption that the form of sure and required perturbations coincides with the first eigenfunction of system oscillations. However, an example is given for the stability of a viscoelastic rod, when the perturbations of initial conditions are more dangerous, if their form differs from the first eigenfunction.This research was sponsored by the Russian Foundation of Fundamental Research of the Russian Academy of Sciences under Grant 94-01-01522.     

结构可靠度分析FORM迭代算法的混沌控制

利用混沌控制原理对FORM收敛失败进行控制. 理清了全局性和局部性两类混沌反馈 控制各种方法的内在联系，说明稳定转换法和自适应调节法属于全局混沌反馈控制 方法，自适应调节法可视为稳定转换法的特例. 参 数调节混合法不过是松弛牛顿法的另一种表达形式，它们都属于局部混沌反馈控制方法. 阐 明了混沌反馈控制表达式与工程力学收敛控制迭代算法的对应关系. 也揭示了这些迭代算法 收敛控制措施的功效和局限性. 提出了一个以稳定转换法为主联合松弛牛顿法的混 沌反馈控制方法，对可靠度分析FORM迭代算法实现了周期振荡、分岔和混沌控制.     

ON THE CONVERGENCE PROBLEMS OF ISHIKAWA AND MANN ITERATIVE PROCESSES WITH ERROR FOR Φ-PSEUDO CONTRACTIVE TYPE MAPPINGS

The purpose of this paper is to introduce the concept of Φ-pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings. The results presented in this paper improve and extend many authors’recent results.     

Bilevel generalized mixed equilibrium problems involving generalized mixed variational-like inequality problems in reflexive Banach spaces

A new bilevel generalized mixed equilibrium problem(BGMEP) involving generalized mixed variational-like inequality problems(GMVLIPs) is introduced and studied in the reflexive Banach spaces.First,an auxiliary generalized mixed equilibrium problem(AGMEP) is introduced to compute the approximate solutions of the BGMEP involving the GMVLIPs.By using a minimax inequality,the existence and the uniqueness of solutions of the AGMEP are proved under mild conditions without any coercive assumptions.By using an au...     

基于Caputo导数的分数阶非线性振动系统响应计算

研究了含分数阶Caputo导数的非线性振动系统响应的数值计算方法。首先,由Caputo分数阶导数算子的叠加关系,得到含分数阶导数项非线性振动系统状态方程的标准形式。其次,基于Caputo导数与Riemann-Liouville导数和Grunwald-Letnikov导数间的关系,推导计算了Caputo导数的一般数值迭代格式。本文方法不要求状态方程中各分数阶导数阶数相等,弱化了已有算法中对分数阶导数阶数的限制,并可推广到多自由度的情形。随后,选择若干有解析解的算例验证了本文方法的正确性。最后,以多吸引子共存的分数阶Duffing振子系统为例,比较Caputo和GL两种算法所得结果,说明了用GL算法求解存在的问题。     

Nonlinear random stability of viscoelastic cable with small curvature

The nonlinear planar mean square response and the random stability of a viscoelastic cable that has a small curvature and subjects to planar narrow band random excitation is studied. The Kelvin viscoelastic constitutive model is chosen to describe the viscoelastic property of the cable material. A mathematical model that describes the nonlinear planar response of a viscoelastic cable with small equilibrium curvature is presented first. And then a method of investigating the mean square response and the almost sure asymptotic stability of the response solution is presented and regions of instability are charted. Finally , the almost sure asymptotic stability condition of a viscoelastic cable with small curvature under narrow band excitation is obtained.     

PREDICTOR-CORRECTOR ALGORITHMS FOR SOLVING GENERALIZED MIXED IMPLICIT QUASI-EQUILIBRIUM PROBLEMS

A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings     

Nonlinear implicit iterative method for solving nonlinear ill-posed problems

In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear implicit iterative method is monotonically decreasing and, with this monotonicity, prove convergence of the new method for both the exact and perturbed equations.     

On the Mann and Ishikawa iterative approximation of solutions to variational inclusions with accretive type mappings in Banach spaces

The purpose of this paper is to introduce and study the existence of solutions and convergence of Mann and Ishikawa iterative processes for a class of variational inclusions with accretive type mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results by Chang, Ding, Hassouni, Kazmi, Siddiqi, Zeng et al. Foundation item: the National Natural Science Foundation of China (19771058)     

An improved SIP scheme for numerical solutions of transonic streamfunction equations

A new improved strongly implicit procedure (SIP) is presented for solving large sets of transonic streamfunction equations with matrix of coefficients [ B ]. This algorithm has several advantages over those now in use. First, Stone's auxiliary matrix [ B ′] is non-symmetric, while in the present scheme the auxiliary matrix [ B ′] is symmetric and the matrix [ B + B ′] is positive definite and symmetric when [ B ] is a symmetric matrix. This ensures the numerical stability of the iterative algorithms. Secondly, for an appropriate choice of iterative parameter ω, the rate of convergence of the new iterative procedure should be faster than the original SIP scheme. Numerical results of the blade-to-blade flows are given with the present scheme. It is shown that the algorithm is efficient and robust.     

Vincent摄动解的收敛上界

本文推证得到了Vincent摄动解与逐次迭代解的一致性,从而由迭代解的收敛性及其收敛上界得到了 Vincent 摄动解的收敛性和收敛上界,同时给出了迭代解的解析特征关系。     

Numerical approximation of optimal control of unsteady flows using SQP and time decomposition

In this paper, we present numerical approximations of optimal control of unsteady flow problems using sequential quadratic programming method (SQP) and time domain decomposition. The SQP method is considered superior due to its fast convergence and its ability to take advantage of existing numerical techniques for fluid flow problems. It iteratively solves a sequence of linear quadratic optimal control problems converging to the solution of the non‐linear optimal control problem. The solution to the linear quadratic problem is characterized by the Karush–Kuhn–Tucker (KKT) optimality system which in the present context is a formidable system to solve. As a remedy various time domain decompositions, inexact SQP implementations and block iterative methods to solve the KKT systems are examined. Numerical results are presented showing the efficiency and feasibility of the algorithms. Copyright © 2004 John Wiley & Sons, Ltd.     

Least-squares-based iterative and gradient-based iterative estimation algorithms for bilinear systems

For bilinear systems with colored noise, this paper gives the input–output representation of the bilinear systems through eliminating the state variables in the model and derives a three-stage gradient-based iterative algorithm and a three-stage least-squares-based iterative algorithm for identifying the parameters of the input–output representation by means of the hierarchical identification principle. A gradient-based iterative (GI) algorithm is given for comparison. Compared with the GI algorithm, the proposed algorithms have lower computational burden and faster convergence speed. The simulation results indicate that the proposed algorithms are more effective for identifying bilinear systems.     

考虑材料应变软化的弹塑性有限元解法研究

指出了已有初应力法多种加速方案在对考虑材料应变软化特性的非线性有限元进行求解时，并不能保证求解过程的收敛性。借鉴整体割线刚度送代法的思想，提出了一种新的初应力加速方案，该方案不仅可以有效地提高初应力法的求解效率，而且即使考虑材料的应变软化，也可以保证在结构达到最大承载能力前的求解过程是收敛的。     

Numerical instabilities and convergence control for convex approximation methods

Convex approximation methods could produce iterative oscillation of solutions for solving some problems in structural optimization. This paper firstly analyzes the reason for numerical instabilities of iterative oscillation of the popular convex approximation methods, such as CONLIN (Convex Linearization), MMA (Method of Moving Asymptotes), GCMMA (Global Convergence of MMA) and SQP (Sequential Quadratic Programming), from the perspective of chaotic dynamics of a discrete dynamical system. Then, the usual four methods to improve the convergence of optimization algorithms are reviewed, namely, the relaxation method, move limits, moving asymptotes and trust region management. Furthermore, the stability transformation method (STM) based on the chaos control principle is suggested, which is a general, simple and effective method for convergence control of iterative algorithms. Moreover, the relationships among the former four methods and STM are exposed. The connection between convergence control of iterative algorithms and chaotic dynamics is established. Finally, the STM is applied to the convergence control of convex approximation methods for optimizing several highly nonlinear examples. Numerical tests of convergence comparison and control of convex approximation methods illustrate that STM can stabilize the oscillating solutions for CONLIN and accelerate the slow convergence for MMA and SQP.