共查询到20条相似文献,搜索用时 62 毫秒
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本文主要解决Banach空间中抽象的半光滑算子方程的解法.提出了两种不精确牛顿法,它们的收敛性同时得到了证明.这两种方法可以看作是有限维空间中已存在的解半光滑算子方程的方法的延伸. 相似文献
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非线性互补问题(NCP)可以重新表述为一个非光滑方程组的解.通过引入一个新的光滑函数,将问题近似为参数化光滑方程组.基于这个光滑函数,我们提出了一个求解P0映射和R0映射非线性互补问题的光滑牛顿法.该算法每次迭代只求解一个线性方程和一次线搜索.在适当的条件下,证明了该方法是全局和局部二次收敛的.数值结果表明,该算法是有效的. 相似文献
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研究一类无限维非线性互补问题的光滑化牛顿法.借助于非线性互补函数,将无限维非线性互补问题转化为一个非光滑算子方程.构造光滑算子逼近非光滑算子,在光滑逼近算子满足方向可微相容性的条件下,证明了光滑化牛顿法具有超线性收敛性. 相似文献
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本文对无穷维空间的映象给出了广义导数的概念,利用这种导数替代光滑映象的Frechet导数,给出了无穷维空间非光滑算子方程的阻尼牛顿法收敛域的一个定理。 相似文献
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本文提出了求解张量互补问题的一类光滑模系矩阵迭代方法.其基本思想是,先将张量互补问题转化为等价的模系方程组,然后引入一个逼近的光滑函数进行求解.我们分析了算法的收敛性,并通过数值实验验证了所提出算法的有效性. 相似文献
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为非线性l1问题的求解构造了光滑逼近函数.首先将非线性l1问题转化为等价的不可微优化问题;其次通过两步提出光滑逼近函数的一般性构造方法;最后进行了数值仿真.文中介绍了光滑逼近函数的有关性质,指出相关文献已有的光滑函数方法是本文的特例,并证明了方法的收敛性及有效性. 相似文献
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本文研究了双曲可压薛定谔映射流(简称HCSM)在n维空间中的奇异解及解的能量特性.使用球极投影,得到了HCSM的一等价方程.该方程存在一有限时间奇异性的解.基于该解,通过精细的分析得到了解的衰减速率和总能量的估计.该奇异解的例子证明了:n维空间中的HCSM存在光滑有限初始能量下的有限时间奇异解. 相似文献
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A solution procedure is presented for a generalization of the standard bottleneck assignment problem in which a secondary criterion is automatically provided. A partitioning problem is modeled by this bottleneck problem to provide an example of its application. 相似文献
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U. Tautenhahn B. Hofmann Y. Shao 《Numerical Functional Analysis & Optimization》2013,34(12):1370-1417
The focus of this article is on conditional stability estimates for ill-posed inverse problems in partial differential equations. Conditional stability estimates have been obtained in related literature by a couple different methods. In this article, we propose a method called interpolation method, which is based on interpolation in variable Hilbert scales. We provide the theoretical background of this method and show that optimal conditional stability estimates are obtained. The capabilities of our method are illustrated by a comprehensive collection of different inverse and ill-posed PDE problems containing elliptic and parabolic problems, one source problem and the problem of analytic continuation. 相似文献
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K. E. Stecke 《Annals of Operations Research》1985,3(1):1-12
The design and use of flexible manufacturing systems (FMSs) involve some intricate operations research problems.FMS design problems include, for example, determining the appropriate number of machine tools of each type, the capacity of the material handling system, and the size of buffers.FMS planning problems include the determination of which parts should be simultaneously machined, the optimal partition of machine tools into groups, allocations of pallets and fixtures to part types, and the assignment of operations and associated cutting tools among the limited-capacity tool magazines of the machine tools.FMS scheduling problems include determining the optimal input sequence of parts and an optimal sequence at each machine tool given the current part mix.FMS control problems are those concerned with, for example, monitoring the system to be sure that requirements and due dates are being met and that unreliability problems are taken care of. This paper defines and describes these FMS problems in detail for OR/MS researchers to work on. 相似文献
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The paper determines the location of the steady state interface between fresh and saltwater in a plane coastal aquifer. The lower boundary is totally impervious while the upper one is impervious below land and semi-pervious below the sea allowing an outflow through this part of the upper boundary. The model equations reduce to two boundary value problems, one valid in x < 0 and the other in x > 0 here x is measured along the aquifer with the origin at the coast. In each region unknown boundaries have to be determined as part of the solution using boundary and continuity conditions. Two cases are presented using the Dupuit approximation. One where the solution can be written down in terms of elementary functions and the other in which we have to use a phase space analysis. 相似文献
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The best strategy for collision avoidance under emergency conditions is to maximize wrt the controls the timewise minimum
distance between the host ship and the intruder ship. In a restricted waterway area, two main constraints must be satisfied:
the lateral deviation of the host ship from the original course is to be contained within certain limits; the longitudinal
distance covered by the host ship is to be subject to a prescribed bound. At the maximin point of the encounter, the time
derivative of the relative distance vanishes; this yields an inner boundary condition (orthogonality between the relative
position vector and the relative velocity vector) separating the main phases of the maneuver: the avoidance and recovery phases.
In this way, the optimal trajectory problem (a Chebyshev problem) can be converted into a Bolza problem with an inner boundary
condition. Numerical solutions are obtained via the multiple-subarc sequential gradient-restoration algorithm (SGRA).
Because the optimal trajectory is not suitable for real-time implementation, a guidance scheme approximating the optimal trajectory
in real time is to be developed. For ship collision avoidance, the optimal trajectory results show that the rudder angle time
history has a bang-bang form characterized by the alternation of saturated control subarcs of opposite signs joined by rapid
transitions. Just as the optimal trajectory can be partitioned into three phases (avoidance phase, recovery phase, steady
phase), a guidance trajectory can be constructed in the same way. For the avoidance and recovery phases, use of decomposition
techniques leads to an algorithm computing the time lengths of these phases in real time. For the steady phase, a feedback
control scheme is used to maneuver the ship steadily. Numerical results are presented.
Portions of this paper were presented by the senior author at the 13th International Workshop on Dynamics and Control, Wiesensteig,
Germany, 22-26 May 2005, in honor of George Leitmann.
This research was supported by NSF Grant CMS-02-18878. 相似文献
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本文提出一种新的数值方法来获得三阶带障碍边值问题的常微分方程的数值解,这类方法的基函数包括三角函数、指数函数、多项式函数。本文将给出一数值例子说明这种方法优于其他差分法、配置法、多项式样条函数法。 相似文献
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In this paper, we consider the problem of minimizing the maximum eigenvalues of a matrix. The aim is to show that this optimization problem can be transformed into a standard nonlinearly constrained optimization problem, and hence is solvable by existing software packages. For illustration, two examples are solved by using the proposed method. 相似文献
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E. R. Panier 《Journal of Optimization Theory and Applications》1989,62(2):279-287
It has been recently reported that minimax eigenvalue problems can be formulated as nonlinear optimization problems involving smooth objective and constraint functions. This result seems very appealing since minimax eigenvalue problems are known to be typically nondifferentiable. In this paper, we show, however, that general purpose nonlinear optimization algorithms usually fail to find a solution to these smooth problems even in the simple case of minimization of the maximum eigenvalue of an affine family of symmetric matrices, a convex problem for which efficient algorithms are available.This work was supported in part by NSF Engineering Research Centers Program No. NSFD-CDR-88-03012 and NSF Grant DMC-84-20740. The author wishes to thank Drs. M. K. H. Fan and A. L. Tits for their many useful suggestions. 相似文献
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Alexander Ženíšek 《Applications of Mathematics》1999,44(1):55-80
Making use of a line integral defined without use of the partition of unity, Green's theorem is proved in the case of two-dimensional domains with a Lipschitz-continuous boundary for functions belonging to the Sobolev spaces W1,p () H1,p () (1 p < ). 相似文献