论文标题
持续重新重新重新制定基数受限优化问题的全球方面
Global aspects of the continuous reformulation for cardinality-constrained optimization problems
论文作者
论文摘要
本文的主要目的是将基数约束优化问题的拓扑相关的固定点及其持续重新进行关联。为此，我们分别专注于非等级M和T-Stationary点。他们所谓的M-和T-Indices唯一地确定了以代数术语考虑的优化问题的全局和局部结构。作为新颖性，我们建议为此目的使持续重新重新重新制定。我们分析的主要结果是，与初始基数约束优化问题相比，正规化连续重新印度的马鞍点的数量呈指数增长。此外，我们通过使用具有正交性类型约束的数学程序的相应结果来获得正规化连续重新重新制定的摩尔斯理论。
The main goal of this paper is to relate the topologically relevant stationary points of a cardinality-constrained optimization problem and its continuous reformulation up to their type. For that, we focus on the nondegenerate M- and T-stationary points, respectively. Their so-called M- and T-indices, which uniquely determine the global and local structure of optimization problems under consideration in algebraic terms, are traced. As novelty, we suggest to regularize the continuous reformulation for this purpose. The main consequence of our analysis is that the number of saddle points of the regularized continuous reformulation grows exponentially as compared to that of the initial cardinality-constrained optimization problem. Additionally, we obtain the Morse theory for the regularized continuous reformulation by using the corresponding results on mathematical programs with orthogonality type constraints.
