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optimality.OF LOCAL MULTILEVEL METHODS FOR ADAPTIVE NONCONFORMING P1 FINITE ELEMENT METHODS

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Journal of Computational Mathematics 2013年第1期31卷 22-46页

作者： Xuejun Xu Huangxin Chen R.H.W. Hoppe LSEC ICMSEC Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100190 China School of Mathematical Sciences Xiamen University Xiamen 361005 China LSEC ICMSEC Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100190 China Department of Mathematics University of Houston Houston TX 77204-3008 USA Institute for Mathematicd University of Augsburg D-86159 Augsburg Germany

In this paper, a local multilevel product algorithm and its additive version are con- sidered for linear systems arising from adaptive nonconforming P1 finite element approx- imations of second order elliptic boundary value problems. The abstract Schwarz theory is applied to analyze the multilevel methods with Jaeobi or Gauss-Seidel smoothers per- formed on local nodes on coarse meshes and global nodes on the finest mesh. It is shown that the local multilevel methods are optimal, i.e., the convergence rate of the multilevel methods is independent of the mesh sizes and mesh levels. Numerical experiments are given to confirm the theoretical results.

关键词： Local multilevel methods Adaptive nonconforming P1 finite element methods,Convergence analysis optimality.

An asymptotically optimal nonparametric adaptive controller

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Science China(Technological Sciences) 2000年第6期43卷 561-568页

作者：郭雷谢亮亮 Institute of Systems Science Chinese Academy of Sciences Beijing 100080 China

For discrete-time nonlinear stochastic systems with unknown nonparametric structure, a kernel estimation-based nonparametric adaptive controller is constructed based on truncated certainty equivalence principle. Global stability and asymptotic optimality.of the closed-loop systems are established without resorting to any external excitations.

关键词： adaptive control nonparametric identification stochastic systems discrete-time optimality.

Direct adaptive control for nonlinear uncertain system based on control Lyapunov function method

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Journal of Systems Engineering and Electronics 2006年第3期17卷 619-623页

作者： Chen Yimei Han Zhengzhi Tang Houjun Dept. of Automation Tianjin Polytechnic Univ. Tianjin 300160 P. R. China School of Electronic Information & Electrical Engineering Shanghai Jiaotong Univ. Shanghai 200030 P. R. China

The problem of adaptive stabilization of a class of multi-input nonlinear systems with unknown parameters both in the state vector-field and the input vector-field has been considered. By employing the control Lyapunov function method, a direct adaptive controller is designed to complete the global adaptive stability of the uncertain system. At the same time, the controller is also verified to possess the optimality. Example and simulations are provided to illustrate the effectiveness of the proposed method.

关键词： adaptive control control Lyapunov function nonlinear uncertain system optimality.

ASYMPTOTIC optimality.FOR ONE CLASS OF TRUNCATED SEQUENTIAL TESTS

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Science China Mathematics 1991年第1期34卷 30-41页

作者：陈家鼎 Department of Probability and Statistics Peking University Beijing 100871 PRC

Suppose that (x_t,t≥0) is a stochastic process of the exponential type with P_θ(x_t∈B) =∫_B exp{θ_x - tψ(θ)}γ(t,x)V_t(dx),where θ∈Θ? (-∞,∞) and V_t is a measure. For testing the hypothesis θ≤θ_0 againstθ>θ_0, we have found a class of truncated sequential tests with probability of the first kindof error not exceeding α, the expected observation time of tests being asymptoticallyminimal as α ↓0.

关键词： stochastic process of exponential type truncated sequential tests asymptotie optimality.

Nondifferentiable Multiobjective Programming under Generalized d-ρ-(η,θ)-Type I Univexity

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Journal of Mathematical Research and Exposition 2011年第4期31卷 655-664页

作者： Chun Feng WANG San Yang LIU Department of Mathematical Sciences Xidian University Shaanxi 710071 P. R. China College of Mathematics and Information Henan Normal University Henan 453007 P. R. China

In this puper, on the basis of notions of d-p-（η, θ）-invex function, type I function and univex function, we present new classes of generalized d-p-（η, θ）-type I univex functions. By using these new concepts, we obtain several sufficient optimality.conditions for a feasible solution to be an efficient solution, and derive some Mond-Weir type duality results.

关键词： multiobjective programming generalized d-p-(η, θ)-type I univexity duality optimality.