Existence of solutions to $$\Gamma $$ Γ -robust counterparts of gap function formulations of uncertain LCPs with ellipsoidal uncertainty sets

Lulin Tan (), Wei Hong Yang () and Jinbiao Pan ()
Additional contact information
Lulin Tan: South China Normal University
Wei Hong Yang: Fudan University
Jinbiao Pan: South China Normal University

Journal of Global Optimization, 2024, vol. 89, issue 1, No 4, 73-92

Abstract: Abstract In this paper, we give some existence theorems of solutions to $$\Gamma $$ Γ -robust counterparts of gap function formulations of uncertain linear complementarity problems, in which $$\Gamma $$ Γ plays a role in adjusting the robustness of the model against the level of conservatism of solutions. If the $$\Gamma $$ Γ -robust uncertainty set is nonconvex, it is hard to prove the existence of solutions to the corresponding robust counterpart. Using techniques of asymptotic functions, we establish existence theorems of solutions to the corresponding robust counterpart. For the case of nonconvex $$\Gamma $$ Γ -robust ellipsoidal uncertainty sets, these existence results are not proved in the paper [Krebs et al., Int. Trans. Oper. Res. 29 (2022), pp. 417–441]; for the case of convex $$\Gamma $$ Γ -robust ellipsoidal uncertainty sets, our existence theorems are obtained under the conditions which are much weaker than those in Krebs’ paper. Finally, a case study for the uncertain traffic equilibrium problem is considered to illustrate the effects of nonconvex uncertainty sets on the level of conservatism of robust solutions.

Keywords: Robust optimization; Linear complementarity problems; Ellipsoidal uncertainty sets; Traffic equilibrium problems; 90C17; 90C33 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10898-023-01340-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jglopt:v:89:y:2024:i:1:d:10.1007_s10898-023-01340-6

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-023-01340-6

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

More articles in Journal of Global Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().