On the role of semismoothness in the implicit programming approach to selected nonsmooth optimization problems

作     者：Gfrerer, Helmut Kočvara, Michal Outrata, Jiří V. 

作者机构： Austrian Academy of Sciences Altenbergerstr. 69 LinzA-404 Austria School of Mathematics University of Birmingham BirminghamB15 2TT United Kingdom Institute of Information Theory and Automation Czech Academy of Sciences Pod vodárenskou věží 4 Prague18208 Czech Republic 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2024年

核心收录：

主　　题：Optimization algorithms 

摘      要：The paper deals with the implicit programming approach to a class of Mathematical Programs with Equilibrium Constraints (MPECs) and bilevel programs in the case when the corresponding reduced problems are solved using a bundle method of nonsmooth optimization. The results obtained allow us to supply the bundle algorithm with suitable, easily computable pseudogradients, ensuring convergence to points satisfying a stationary condition. Both the theory and computational implementation heavily rely on the notion of SCD (subspace containing derivatives) mappings and the associated calculus. The approach is validated via a complex MPEC with equilibrium governed by a variational inequality of the 2nd kind and by an academic bilevel program with a nonsmooth upper-level *** Codes 65K10, 65K15, 90C26 © 2024, CC BY.