标题： 二阶倾斜稳定性在复合优化中的表征 显示英文标题

标题： Second-Order Characterizations of Tilt Stability in Composite Optimization

摘要： 倾斜稳定性是变分分析和优化中的基本概念，在理论问题和数值计算中起着关键作用。 本文研究了有限维空间中一类一般复合优化问题的局部极小值点的倾斜稳定性，其中扩展实值目标函数是抛物正则和光滑函数的复合。 在最弱的度量次正则约束条件和其他可验证条件下，我们通过二阶广义微分建立了倾斜稳定性的统一邻域和点基表征。 所得结果为优化及相关领域的变分稳定性与数值算法的进一步发展提供了严格的理论基础。 显示英文摘要

摘要： Tilt stability is a fundamental concept of variational analysis and optimization that plays a pivotal role in both theoretical issues and numerical computations. This paper investigates tilt stability of local minimizers for a general class of composite optimization problems in finite dimensions, where extended-real-valued objectives are compositions of parabolically regular and smooth functions. Under the weakest metric subregularity constraint qualification and other verifiable conditions, we establish unified neighborhood and pointbased characterizations of tilt stability via second-order generalized differentiation. The obtained results provide a rigorous theoretical foundation for further developments on variational stability and numerical algorithms of optimization and related topics.