This is a special issue on Quaternion Optimization and Dual Quaternion Optimization, with guest editors: Zhenghai Huang, Chen Ling, Ziyan Luo and Xinzhen Zhang.

Preface: Zheng-Hai Huang, Chen Ling, Ziyan Luo and Xinzhen Zhang

Renjie Xu, Yimin Wei
Randomized quaternion matrix UTV decomposition and its applications in quaternion matrix optimization

Can Li, Yannan Chen and Donghui Li
A proximal linearized algorithm for dual quaternion optimization with applications in hand-eye calibration

Chen Ling, Hongjin He, Liqun Qi and Tingting Feng
Spectral norm and von Neumann type trace inequality for dual quaternion matrices

Hongxing Wang, Pei Huang and Chong Cui
Perfect Hermitian matrix and dual quaternion Löwner partial orders

Si-Tao Ling, Zhe-Han Hu, Bing Yang, Yi-Ding Li
Color linear discriminant analysis for face recognition based on quaternion model

Wenxin Hu, Yajing Wang and Xiangke Wang
Unit dual quaternion based tracking control with velocity saturations applied on quadrotor

Weihua Chen, Caiqin Song and Meirong Xu
STP method for solving the minimal norm Toeplitz solutions of $MX- N = GY + R$

Dandan Wang and Haifeng Ma
Perturbations of group inverses of quaternion tensors under the QT-product

Sheng Chen and Haofei Hu
Unitarily invariant norms on dual quaternion matrices