一种用于弹性类型张量极端M-特征值的高效内存梯度方法

An adaptive cubic regularization method for computing extreme eigenvalues of tensors

In this paper, we compute the H- and Z-eigenvalues of even order symmetric tensors by using the adaptive cubic regularization algorithm.

Shape and Topology Optimization involving the eigenvalues of an elastic structure: A multi-phase-field approach

A cost functional involving the eigenvalues of an elastic structure, that is described by a multi-phase-field equation, is optimized. This allows us to handle topology changes and multiple materials. We prove continuity and differentiability of the eigenvalues and we establish the existence of a global minimizer to our optimization problem. We further derive first-order necessary optimality conditions for local minimizers. Moreover, an optimization problem combining eigenvalue and compliance optimization is also discussed.

关于厄米矩阵极端特征值的免正交化共轭梯度法的收敛性：一种黎曼优化解释

On the convergence of orthogonalization-free conjugate gradient method for extreme eigenvalues of Hermitian matrices: a Riemannian optimization interpretation

本文证明求解无约束 Burer-Monteiro 公式的非线性共轭梯度法等价于 Bures-Wasserstein 度量下商流形上的黎曼共轭梯度法，从而证明其全局收敛性，并通过数值实验验证了其在大规模厄米矩阵极端特征值计算中的高效性。

On a classical spectral optimization problem in linear elasticity

We consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the $N$-dimensional Euclidean space. We survey recent results concerning the analytic dependence of the elementary symmetric functions of the eigenvalues upon domain perturbation and the role of balls as critical points of such functions subject to volume constraint. Our discussion concerns Dirichlet and buckling-type problems for polyharmonic operators, the Neumann and the intermediate problems for the biharmonic operator, the Lamé and the Reissner-Mi…

椭圆算子第一特征值的伪凹优化及其在均匀化拓扑优化中的应用

Pseudo-concave optimization of the first eigenvalue of elliptic operators with application to topology optimization by homogenization

研究线性椭圆算子第一特征值优化问题，证明其关于密度类参数的伪凹性，此性质可得出最大化问题驻点即全局最大值点，在电导率设置中有0-1极小值点，并通过数值实验验证理论结果。

高维极端特征值问题：低秩张量参数化与优化

High-dimensional extreme eigenvalue problems: low-rank tensor parametrization and optimization

针对高维极端特征值问题，本文提出基于张量列格式的低秩参数化与流形优化方法，显著降低计算成本，并在多个数值实验中达到全空间求解器精度且具备鲁棒性。