Extended convergence analysis of the Scholtes-type regularization for cardinality-constrained optimization problems
本文扩展了基数约束优化问题中Scholtes型正则化方法的收敛性分析，揭示了其在鞍点附近的行为，并证明了该方法在非退化T稳定点附近有良好定义，且收敛点的拓扑类型保持不变。
Abstract 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. As consequence, we conclude that the global structure of the Scholtes-type regularization essentially coincides with that of CCOP.