论文标题
用于基数受限优化问题的Scholtes型正则化的扩展收敛分析
Extended convergence analysis of the Scholtes-type regularization for cardinality-constrained optimization problems
论文作者
论文摘要
我们扩展了Scholtes-type正则化方法的收敛分析，以解决基数限制的优化问题。它的行为在马鞍点的附近阐明，而不仅仅是在文献中所做的那样。通过用作中间步骤，这是可能的，最近引入了对基数受限的优化问题的正规化连续重新印度。我们表明，Scholtes-type正则化方法在该正则化连续重新制定的非等级t平稳地点周围是局部定义的。此外，相应的scholtes-type正则化的非排定karush-kuhn-tucker点会收敛到具有相同索引的T站点，即其拓扑类型持续存在。总体而言，我们得出的结论是，正规化持续重新制定及其Scholtes型正则化的全球结构基本上是重合的。
We extend the convergence analysis of the Scholtes-type regularization method for cardinality-constrained optimization problems. Its behavior is clarified in the vicinity of saddle points, and not just of minimizers as it has been done in the literature before. This becomes possible by using as an intermediate step the recently introduced regularized continuous reformulation of a cardinality-constrained optimization problem. We show that the Scholtes-type regularization method is well-defined locally around a nondegenerate T-stationary point of this regularized continuous reformulation. Moreover, the nondegenerate Karush-Kuhn-Tucker points of the corresponding Scholtes-type regularization converge to a T-stationary point having the same index, i.e. its topological type persists. Overall, we conclude that the global structure of the regularized continuous reformulation and its Scholtes-type regularization essentially coincide.
