We introduce three kinds of new weighted quaternion-matrix minimization problems in order to extend some well-known constrained approximation problems. The main result is the claim that these new minimization problems have unique solutions which are expressed in terms of expressions involving weighted core-EP inverse and its dual for adequate quaternion matrices. Also, determinantal expressions of solutions for considered minimization problems are given. Obtained theoretical results are justified by a numerical example.

中文翻译：

---

四元数矩阵的加权最小化问题

我们引入了三种新的加权四元数矩阵最小化问题，以扩展一些众所周知的约束逼近问题。主要结果是声称这些新的最小化问题具有独特的解决方案，这些解决方案以涉及加权核心 EP 逆及其对足够四元数矩阵的对偶的表达式表示。此外，还给出了所考虑的最小化问题的解决方案的行列式表达式。得到的理论结果由数值例子证明。