同时采用对偶方法来避免全变分项的非光滑性和高非线性性。
The algorithm also adopts dual method to avoid the nonsmooth and highly nonlinearity of total variation term.
本文对不等式约束非线性规划提出一种光滑逼近- BFGS法。
In this paper, a smooth approximation-BFGS method for solving inequality constrained nonlinear programming is presented.
利用二阶的非线性扩散方程进行图像去噪易产生具有“阶越效应”的去噪结果，也即使分段光滑的图像变为分段常量的。
Image denoising with second order non-linear diffusion PDEs often leads to an undesirable staircase effect, namely, the transformation of smooth regions into piecewise constant ones.
分形理论主要描述自然界和非线性系统中不光滑和不规则的几何形体，它为植物形态的模拟提供了描述语言和理论基础。
Fractal theory mainly describes the nature and nonlinear system objects which are not smooth and irregular, it also provides description language and theoretical basis for plant simulation.
分形维数是描述自然界和非线性系统中不光滑和不规则几何体的有效工具，是所有分形对象的主要特征之一。
Fractal dimension is usually an effective way that used to describe the non-smooth and non-regular geometry objects in the nature and non-liner systems.
这个差异可能由分段光滑映象函数的非线性造成。
And this difference may be induced by the nonlinear function of piecewise-smooth map.
研究一般的仿射非线性联级系统的全局光滑可镇定。
In this paper, the global stabilization of the general nonlinear cascaded systems is studied.
提出了新的弱正则伪光滑非线性互补(ncp)函数，该函数具有良好的性质。
In this paper, we present a new nonlinear complementarity (NCP) function which is piecewise linear-rational, regular pseudo-smooth and has nice properties.
为了研究不连续系统中的混沌行为，观察一个由比较器控制的，带有模拟开关的RLC非线性电路模型，此电路系统的行为可以用一个分段光滑映象来描述。
In order to study the chaotic behavior in the discontinuous system, a RLC nonlinear circuit model with an analogy switch was observed, which was described by a piecewise-continuous map.
针对非线性互补问题，提出了与其等价的非光滑方程的一个下降算法，并在一定条件下证明了该算法的全局收敛性。
This paper presents a new descend algorithm for nonlinear complementarity problems. The global convergence of the algorithm is proved under milder conditions.
分形理论是非线性系统理论中最为活跃的分支之一，研究的是复杂系统产生的不光滑、不可微分的复杂几何体。
Fractal theory is the most active branch of the non-linear science, what it concerns is non-smooth and non-differential geometry produced by complex systems.
讨论了非线性奇异扩散方程的第二初边值问题，证明了存在唯一的光滑解，且解关于初值是连续依赖的。
In this paper, the second initial and boundary value problem of a nonlinear singular diffusion equation is discussed.
提出了求解非线性互补问题的一个光滑逼近算法，在一定条件下证明了该算法的全局收敛性。
A smoothing approximation algorithm for nonlinear complementarity problems was introduced and the global convergence of the algorithm was proved under milder conditions.
对束方法的研究涉及凸分析，线性和非线性规划，非光滑分析等数学分支。
Researches on bundle methods touch upon such mathematical branches as convex analysis, nonlinear programming and nonsmooth analysis.
利用凝聚函数一致逼近非光滑极大值函数的性质，将非线性互补问题转化为参数化光滑方程组。
By using a smooth aggregate function to approximate the non-smooth max-type function, nonlinear complementarity problem can be treated as a family of parameterized smooth equations.
针对这一优化问题，通过引入非线性互补问题函数，将原优化问题转化为非线性方程组，并采用半光滑牛顿法进行求解。
By introducing nonlinear complementarity problem function, the original optimization problem is transferred equivalently to a set of nonlinear equations and solved by semi-smooth Newton method.
本文就此类问题展开深入研究，提出几种能克服不光滑非线性影响的控制系统设计方法，并将所提出的控制方法应用到空地导弹控制系统中。
This paper deeply studies these problems. Several methods of the control of systems with nonsmooth nonlinearities are presented and applied to air-ground missile system.
带不等式约束的非线性规划，其KKT条件可以通过NCP函数转化为一个非光滑的方程组，然后用熵光滑化函数光滑化，得到一个带参数的方程组。
The KKT conditions of a nonlinear programming with linear inequality constrains can be transformed into a system of equations by NCP function. Then it is smoothed by Entropy smoothing function.
另一方面，采用传统迭代子和共轭梯度法作为光滑子，我们证明了瀑布型多重网格法对一、二维非线性椭圆边值问题，在能量范数下，均可获得最优收敛阶。
Onthe other hand, with traditional iterations and the conjugate gradient(CG) as smoothers, we can show the optimal convergence rate of the cascadic method in energy norm for 1-D and 2-D cases.
新模型由差分动态系统和非线性互补函数（NCP）转换的半光滑方程系统构成。
The new model is composed of difference dynamic system and semi-smooth equations reformulated by NCP.
新模型由差分动态系统和非线性互补函数（NCP）转换的半光滑方程系统构成。
The new model is composed of difference dynamic system and semi-smooth equations reformulated by NCP.
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