共查询到20条相似文献,搜索用时 31 毫秒
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本文研究了文献[1]所引入的Orlicz投影体问题.利用Orlicz投影体在线性变换下的不变性,获得了椭球的Orlicz投影体仍是椭球的结果.作为例子,计算了当取两个特定的凸函数时单位球的Orlicz投影体的支持函数. 相似文献
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Comparing the volume of the projection body of a double cone and that of the projection body of a ball, we give an explicit counter-example for the Shephard problem of convex bodies in Rn (n ≥ 3) and an affirmative answer to the question of Zhang. 相似文献
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Natalia Chinchaladze 《复变函数与椭圆型方程》2018,63(6):886-895
Vibration problem of an antiplane strain (shear) of orthotropic non-homogeneous prismatic shell-like bodies is considered when the shear moduli depending on the body projection (i.e. on a domain lying in the plane of interest) variables may vanish on a part of the boundary of the projection. 相似文献
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本文研究了关于投影不等式的Petty猜想这个凸体理论中的一个著名公开问题.利用凸体的Lp-Brunn-Minkowski-Firey理论,建立了Petty投影不等式猜想的Lp-版本的几个不同精度的不等式,推广了已有文献的结论. 相似文献
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We consider the second-order projection schemes for the time-dependent natural convection problem. By the projection method, the natural convection problem is decoupled into two linear subproblems, and each subproblem is solved more easily than the original one. The error analysis is accomplished by interpreting the second-order time discretization of a perturbed system which approximates the time-dependent natural convection problem, and the rigorous error analysis of the projection schemes is presented. Our main results of the second order projection schemes for the time-dependent natural convection problem are that the convergence for the velocity and temperature are strongly second order in time while that for the pressure is strongly first order in time. 相似文献
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并行技术在约束凸规划化问题的对偶算法中的应用 总被引:1,自引:0,他引:1
用 Rosen(196 1)的投影梯度的方法求解约束凸规划化问题的对偶问题 ,在计算投影梯度方向时 ,涉及求关于原始变量的最小化问题的最优解 .我们用并行梯度分布算法 (PGD)计算出这一极小化问题的近似解 ,证明近似解可以达到任何给定的精度 ,并说明当精度选取合适时 ,Rosen方法仍然是收敛的 相似文献
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S. E. Zhelezovskii 《Computational Mathematics and Mathematical Physics》2006,46(8):1387-1398
The Cauchy problem for a system of two operator-differential equations is considered that is an abstract statement of linear coupled thermoelasticity problems. Error estimates in the energy norm for the semidiscrete Galerkin method as applied to the Cauchy problem are established without imposing any special conditions on the projection subspaces. By way of illustration, the error estimates are applied to finite element schemes for solving the coupled problem of plate thermoelasticity considered within the framework of the Kirchhoff linearized theory. The results obtained are also applicable to the case when the projection subspaces in the Galerkin method (for the original abstract problem) are the eigenspaces of operators similar to unbounded self-adjoint positive definite operator coefficients of the original equations. 相似文献
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V. I. Zorkal’tsev 《Computational Mathematics and Mathematical Physics》2018,58(5):813-821
In computational methods and mathematical modeling, it is often required to find vectors of a linear manifold or a polyhedron that are closest to a given point. The “closeness” can be understood in different ways. In particular, the distances generated by octahedral, Euclidean, and Hölder norms can be used. In these norms, weight coefficients can also be introduced and varied. This paper presents the results on the properties of a set of octahedral projections of the origin of coordinates onto a polyhedron. In particular, it is established that any Euclidean and Hölder projection can be obtained as an octahedral projection due to the choice of weights in the octahedral norm. It is proven that the set of octahedral projections of the origin of coordinates onto a polyhedron coincides with the set of Pareto-optimal solutions of the multicriterion problem of minimizing the absolute values of all components. 相似文献
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Minkowski's projection bodies have evolved into Lp projection bodies and their asymmetric analogs. These all turn out to be part of a far larger class of Orlicz projection bodies. The analog of the classical Petty projection inequality is established for the new Orlicz projection bodies. 相似文献
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J. C. Geromel L. F. B. Baptistella 《Journal of Optimization Theory and Applications》1981,35(2):231-249
In this paper, we propose a feasible-direction method for large-scale nonconvex programs, where the gradient projection on a linear subspace defined by the active constraints of the original problem is determined by dual decomposition. Results are extended for dynamical problems which include distributed delays and constraints both in state and control variables. The approach is compared with other feasible-direction approaches, and the method is applied to a power generation problem. Some computational results are included.This work was supported by the Conselho Nacional de Desenvolvimento Cientifico e Tecnologico, Brasilia, Brasil, and by the Fundaçao de Amparo a Pesquisa do Estado de Sao Paulo, Sao Paulo, Brazil.On leave from UNICAMP, Campinas, Brazil. 相似文献
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G. Landi E. Loli Piccolomini 《Applied mathematics and computation》2011,218(5):2091-2107
In this work, the problem of the restoration of images corrupted by space invariant blur and noise is considered. This problem is ill-posed and regularization is required. The image restoration problem is formulated as a nonnegatively constrained minimization problem whose objective function depends on the statistical properties of the noise corrupting the observed image. The cases of Gaussian and Poisson noise are both considered. A Newton-like projection method with early stopping of the iterates is proposed as an iterative regularization method in order to determine a nonnegative approximation to the original image. A suitable approximation of the Hessian of the objective function is proposed for a fast solution of the Newton system. The results of the numerical experiments show the effectiveness of the method in computing a good solution in few iterations, when compared with some methods recently proposed as best performing. 相似文献
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将经典的对偶混合体积概念推广到Lp空间,提出了"q-全对偶混合体积"的概念.将传统的P≥1的Lp投影体概念拓展,提出P<1时的Lp投影体和混合投影体概念,并且建立了Lp-极投影Brunn-Minkowski不等式.作为应用,推广了熟知的极投影Brunn-Minkowski不等式,获得了投影Brunn-Minkowski不等式的Lp空间的极形式. 相似文献
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解非线性约束拟凸规划的一个梯度投影法 总被引:4,自引:0,他引:4
目前国内外所流行的梯度投影法(包括Rosen的原有算法和一些修正算法)还存在以下几个问题:一、要增加Polak程序以保证算法的收僉性。二、在计算投影梯度时,每步一般要作两次投影。三、对于非线性约束问题,负梯度投影方向是不可行的,因此必须在此方向的基础上构造出能保证算法收歛的新可行下降方向。而目前为构造出这个新方向所作的计算都比较复杂。 1981年[5]提出了一个处理线性约束条件的梯度投影法,基本上解决了线 相似文献
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马国栋 《数学物理学报(A辑)》2020,(3):641-649
该文考虑求解带非线性不等式和等式约束的极大极小优化问题,借助半罚函数思想,提出了一个新的广义投影算法.该算法具有以下特点:由一个广义梯度投影显式公式产生的搜索方向是可行下降的;构造了一个新型的最优识别控制函数;在适当的假设条件下具有全局收敛性和强收敛性.最后,通过初步的数值试验验证了算法的有效性. 相似文献