We propose an optimization approach to the solution of the partial quadratic eigenvalue assignment problem (PQEVAP) for active vibration control design with robustness (RPQEVAP). The proposed cost function is based on the concept of sensitivities over the sum and the product of the closed-loop eigenvalues, introduced recently in our paper. Explicit gradient formula for the solutions using state feedback and derivative feedback are derived as functions of a free parameter. These formulas are then used to build algorithms to solve RPQEVAP in a numerically efficient way, with no need to compute new eigenvectors, for both state feedback and state-derivative feedback designs. Numerical experiments are carried out in order to demonstrate the effectiveness of the algorithms and to compare the proposed method with other methods in the literature, thus showing its effectiveness.
The quadratic assignment problem: the linearization of Xia and Yuan is weaker than the linearization of Adams and Johnson and a family of cuts to narrow the gap
Eigenvalue, Quadratic Programming, and Semidefinite Programming Bounds for a Cut Minimization Problem
考虑将图的节点集划分为给定大小的$k$集，从而得到使用（去除）第$k$集得到的\emph{minimize the cut}的问题.如果得到的割具有值$0$，那么我们得到了顶点分隔符。这个问题与图的划分问题密切相关。事实上，我们使用的模型与图划分问题的模型相同，除了不同的\emph{quadratic}目标函数。我们期待在已知的和新的界限，从各种放宽这个NP-困难的问题。这包括：标准特征值界、使用邻接矩阵和拉普拉斯算子的投影特征值界、基于最近成功的二次指派问题的二次规划（QP）界的QP界、以及半定规划界。我们包括大型和\emph{huge}的问题，说明在强度和时间方面的边界的效率的数值测试。
Relative-Interior Solution for the (Incomplete) Linear Assignment Problem with Applications to the Quadratic Assignment Problem
Faculty of Electrical Engineering, Czech Technical University in Prague（捷克技术大学布拉格分校电子工程系）；Computer Vision and Learning Lab, IWR, University of Heidelberg（海德堡大学计算机视觉与学习实验室）
Variational quantum algorithms for permutation-based combinatorial problems: Optimal ansatz generation with applications to quadratic assignment problems and beyond
Institut Polytechnique de Paris（巴黎理工学院）；ENSTA（国立高等先进技术学院）；UMA（应用数学实验室）；Conservatoire National des Arts et Métiers（国立工艺博物馆）；CEDRIC（计算机科学与数字系统研究中心）；École Nationale Supérieure d’Informatique pour l’Industrie et l’Entreprise（工业与企业高级信息学院）
Exact Quadratic Penalty Function for Symplectic Eigenvalue Problem
State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院计算数学与科学工程计算国家重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）；School of Data Science, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）数据科学学院）
Hardware-Compatible Single-Shot Feasible-Space Heuristics for Solving the Quadratic Assignment Problem
QB Information Technologies (1QBit)（1QB信息技术公司）；Institute for Neuromorphic Compute Nodes (PGI-14), Peter Grünberg Institute, Forschungszentrum Jülich GmbH（于利希研究中心彼得·格林贝格研究所神经形态计算节点研究所）；RWTH Aachen University（亚琛工业大学）；HPE Labs, Hewlett Packard Enterprise（惠普企业实验室）；University of California, Santa Barbara（加州大学圣塔芭芭拉分校）
Learning to Solve the Quadratic Assignment Problem with Warm-Started MCMC Finetuning
School of Mathematical Science, Peking University（北京大学数学科学学院）；State Key Laboratory of Mathematical Sciences, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院数学科学国家重点实验室）；Beijing International Center for Mathematical Research, Peking University（北京大学北京国际数学研究中心）
On Partial Optimality in QUBO via Quadratic Posiform Autarkies
TU Dresden（德累斯顿工业大学）；Faculty of Computer Science, TU Dresden（德累斯顿工业大学计算机学院）；Center for Scalable Data Analytics and AI, Dresden/Leipzig（德累斯顿/莱比锡可扩展数据分析与人工智能中心）
