论文标题
一类对Riemannian歧管及其应用的非平滑光滑优化的隔离平静
On the robust isolated calmness of a class of nonsmooth optimizations on Riemannian manifolds and its applications
论文作者
论文摘要
本文研究了Riemannian歧管上的一类非平滑优化问题的KKT溶液映射的强大孤立平静特性。鲁滨逊约束资格，严格的鲁滨逊约束资格和第二阶条件的歧管版本被定义和讨论。我们表明，KKT溶液映射的稳健孤立平静相当于满足M-SRCQ和M-SOSC条件。此外，在上述两个条件下，我们表明Riemannian增强拉格朗日方法达到了局部线性收敛速率。最后，我们验证了所提出的条件，并证明了在球体上两个最小化问题和固定级别矩阵的歧管上的收敛速率。
This paper studies the robust isolated calmness property of the KKT solution mapping of a class of nonsmooth optimization problems on Riemannian manifolds. The manifold versions of the Robinson constraint qualification, the strict Robinson constraint qualification, and the second order conditions are defined and discussed. We show that the robust isolated calmness of the KKT solution mapping is equivalent to satisfying the M-SRCQ and M-SOSC conditions. Furthermore, under the above two conditions, we show that the Riemannian augmented Lagrangian method achieves a local linear convergence rate. Finally, we verify the proposed conditions and demonstrate the convergence rate on two minimization problems over the sphere and the manifold of fixed rank matrices.
