On the role of semismoothness in the implicit programming approach to selected nonsmooth optimization problems
Abstract
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 objective.
Cite
@article{arxiv.2412.05953,
title = {On the role of semismoothness in the implicit programming approach to selected nonsmooth optimization problems},
author = {Helmut Gfrerer and Michal Kočvara and Jiří V. Outrata},
journal= {arXiv preprint arXiv:2412.05953},
year = {2024}
}
Comments
arXiv admin note: text overlap with arXiv:2405.14637