Geometric methods are important for researching the differential properties of metric projectors, sensitivity analysis, and the augmented Lagrangian algorithm. Sun [3] researched the relationship among the strong second-order sufficient condition, constraint nondegeneracy, B-subdifferential nonsingularity of the KKT system, and the strong regularity of KKT points in investigating nonlinear semidefinite programming problems. Geometric properties of cones are necessary in studying second-order sufficient condition and constraint nondegeneracy. In this paper, we study the geometric properties of a class of nonsymmetric cones, which is widely applied in optimization problems subjected to the epigraph of vector k-norm functions and low-rank-matrix approximations. We compute the polar, the tangent cone, the linear space of the tangent cone, the critical cone, and the affine hull of this critical cone. This paper will support future research into the sensitivity and algorithms of related optimization problems.

中文翻译：

---

一类非对称锥的几何性质

几何方法对于研究公制投影仪的差分特性，灵敏度分析和增强拉格朗日算法非常重要。Sun [3]研究了非线性半定规划问题中强二阶充分条件，约束非简并，B-亚微分非奇异性与KKT系统的强正则性之间的关系。圆锥的几何特性对于研究二阶充分条件和约束非简并性是必要的。在本文中，我们研究了一类非对称圆锥的几何性质，该性质广泛应用于向量k范数函数和低秩矩阵逼近的最优化问题。我们计算极点，切线锥，切线锥的线性空间，临界锥，以及该临界锥的仿射外壳。本文将为将来对相关优化问题的敏感性和算法的研究提供支持。