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The Improvement Function Reformulation for Graphs of Minimal Point Mappings

Schwarze, Stefan ORCID iD icon 1; Stein, Oliver 1
1 Institut für Operations Research (IOR), Karlsruher Institut für Technologie (KIT)

Abstract:

Graphs of minimal point mappings of parametric optimization problems appear in the definition of feasible sets of bilevel optimization problems and of semi-infinite optimization problems, and the intersection of multiple such graphs defines (generalized) Nash equilibria. This paper shows how minimal point graphs of nonconvex parametric optimization problems can be enclosed with the help of well structured problems with additional parameters. This enclosure coincides with the minimal point graph under
mild assumptions. We specify our results to the setting of generalized Nash equilibrium problems. This well structured formulation of the enclosure makes it accessible to approximations by branch-and-bound methods. We provide corresponding numerical results in a separate paper.


Verlagsausgabe §
DOI: 10.5445/IR/1000190953
Veröffentlicht am 24.02.2026
Originalveröffentlichung
DOI: 10.1007/s10957-025-02911-1
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Operations Research (IOR)
Publikationstyp Zeitschriftenaufsatz
Publikationsmonat/-jahr 03.2026
Sprache Englisch
Identifikator ISSN: 0022-3239, 1573-2878
KITopen-ID: 1000190953
Erschienen in Journal of Optimization Theory and Applications
Verlag Springer
Band 208
Heft 3
Seiten Art.-Nr.: 99
Vorab online veröffentlicht am 18.02.2026
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