共查询到20条相似文献,搜索用时 578 毫秒
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本文提出了一个解线性等式约束优化问题的新锥模型信赖域方法.论文采用零空间技术消除了新锥模型子问题中的线性等式约束,用折线法求解转换后的子问题,并给出了解线性等式约束优化问题的信赖域方法.论文提出并证明了该方法的全局收敛性,并给出了该方法解线性等式约束优化问题的数值实验.理论和数值实验结果表明新锥模型信赖域方法是有效的,这给出了用新锥模型进一步研究非线性优化的基础. 相似文献
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Di Pillo和Grippo提出的含参数C〉0的增广Lagrangian函数中,使用了最大函数,该函数可能在无穷多个点处不可微.为了克服这个问题,濮定国在2004年提出了一类带新的NCP函数的乘子法.该方法在增广Lagrangian函数和原问题之间存在很好的等价性;同时该方法具有全局收敛性,且在适当假设下,具有超线性收敛率.但是在该方法中,要求参数C充分大.为了实现算法及提高算法效率,本文给出了一个有效选择参数C的方法. 相似文献
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求解非线性互补问题的一个非精确信赖域方法 总被引:2,自引:1,他引:1
本文研究了基于非线性互补问题的等价非光滑优化问题的非精确依赖域方法,利用非线性规划的理论和方法,在一定条件下,获得了该方法的全局收敛性结果. 相似文献
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本文研究了声波散射区域的重建,给上散射波的叠加重建散射区域的一个方法,该方法利用散射波的叠加,将声波障碍反散射这个非一不适定问题分两步处理,第一步求解一个第一类线性积分方程。第二步求解一个非线性最优化问题,我们证明了该方法的收敛性。 相似文献
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This paper is concerned with efficient numerical methods for solving the time-dependent scattering and inverse scattering problems of acoustic waves in a locally perturbed half-plane. By symmetric continuation, the scattering problem is reformulated as an equivalent symmetric problem defined in the whole plane. The retarded potential boundary integral equation method is modified to solve the forward problem. Then we consider the inverse scattering problem of determinating the local perturbation from the measured scattered data. The time domain linear sampling method is employed to deal with the inverse problem. The computation schemes proposed in this paper are relatively simple and easy to implement. Several numerical examples are presented to show the effectiveness of the proposed methods. 相似文献
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Deyue Zhang Yukun Guo Chengchun Gong Guan Wang 《Advances in Computational Mathematics》2012,36(1):3-20
The scattering of time-harmonic electromagnetic waves propagating in a homogeneous chiral environment by obstacles is studied.
The problem is simplified to a two-dimensional scattering problem, and the existence and the uniqueness of solutions are discussed
by a variational approach. The diffraction problem is solved by a finite element method with perfectly matched absorbing layers.
Our computational experiments indicate that the method is efficient. 相似文献
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Deyue Zhang Fuming Ma 《高等学校计算数学学报(英文版)》2006,15(2):164-179
1 Introduction The phenomenon of optical activity in special materials has been known since the beginning of the last century. Whereas optical activity has been considered in optics and in quantum mechanics for many years, its analysis within the framewor… 相似文献
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A Bäcklund transformation both in bilinear form and in ordinary form for the transformed Vakhnenko equation is derived. An inverse scattering problem is formulated. The inverse scattering method has a third-order eigenvalue problem. A procedure for finding the exact N-soliton solution of the Vakhnenko equation via the inverse scattering method is described. The procedure is illustrated by considering the cases N=1 and N=2. 相似文献
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Alain L. Fymat 《Applied mathematics and computation》1975,1(2):131-185
The possibility of remotely sensing the optical properties of scattering particulates from the variations in either the angular or the spectral characteristics, or both, of the radiation they transmit or scatter, is a problem of fundamental importance in the monitoring of environmental particulate pollution. It is shown that the corresponding problem is (or can be brought to) one of inverting first kind Fredholm integral equations. The solution to this problem would also enable one to follow the dynamical evolution of the polluted environment if it can be obtained in a time scale that is comparable to, or shorter than, the time constant of the physical measurements.The direct problem of how given physical parameters of such particles affect the transmission and scattering of incident radiation is first analyzed on the basis of the corresponding radiative transfer problem, including single and multiple scattering, and polarization induced on scattering. The various available methods for reconstructing the size distribution from the observed directly transmitted or scattered light are reviewed, particularly with regard to their main advantages and shortcomings. For direct light transmission, these include: library, iterative, and least-squares methods; the trial-and-error method; the matrix inversion method with smoothing constraint (MIM); the resolution accuracy trade-off method; and the analytical method. A minimization search method with smoothing constraint, an essential modification to the MIM, is also proposed. The corresponding methods for singly and multiply scattered light are likewise reviewed. The proposed forward-scattering method is shown to provide excellent reconstructions from either angular or spectral light measurements under proper experimental conditions. It can also be coupled with a minimization search in order to provide simultaneously the complex refractive index of the particles. The potentialities of other methods for the complete multiple scattering problem—the minimization search method, quasilinearization method, and small-angle Gaussian approximation method—are also studied. 相似文献
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This paper presents a volume integral equation method for an electromagnetic scattering problem for three-dimensional Maxwell's equations in the presence of a biperiodic, anisotropic, and possibly discontinuous dielectric scatterer. Such scattering problem can be reformulated as a strongly singular volume integral equation (i.e., integral operators that fail to be weakly singular). In this paper, we firstly prove that the strongly singular volume integral equation satisfies a Gårding-type estimate in standard Sobolev spaces. Secondly, we rigorously analyze a spectral Galerkin method for solving the scattering problem. This method relies on the periodization technique of Gennadi Vainikko that allows us to efficiently evaluate the periodized integral operators on trigonometric polynomials using the fast Fourier transform (FFT). The main advantage of the method is its simple implementation that avoids for instance the need to compute quasiperiodic Green's functions. We prove that the numerical solution of the spectral Galerkin method applied to the periodized integral equation converges quasioptimally to the solution of the scattering problem. Some numerical examples are provided for examining the performance of the method. 相似文献
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Problems for electromagnetic scattering are of significant importance in many areas of technology. In this paper we discuss the scattering problem of electromagnetic wave incident by using boundary element method associated with splines. The problem is modelled by a boundary value problem for the Helmholtz eouation 相似文献
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D.J Kaup 《Journal of Mathematical Analysis and Applications》1976,54(3):849-864
By solving the inverse scattering problem for a third-order (degenerate) eigenvalue problem, we can find the closure of the squared eigenfunctions of the Zakharov-Shabat equations. The question of the completeness of squared eigenstates occurs in many aspects of “inverse scattering transforms” (solving nonlinear evolution equations exactly by inverse scattering techniques) as well as in various aspects of the inverse scattering problem. The method we use is quite suggestive as to how one might find the closure of the squared eigenfunctions of other eigenvalue equations, and we point the strong analogy between our results and the problem of finding the closure of the eigenvectors of a nonself-adjoint matrix. 相似文献