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Convergent upper bounds in global minimization with nonlinear equality constraints

Füllner, Christian 1; Kirst, Peter 1; Stein, Oliver ORCID iD icon 1
1 Institut für Operations Research (IOR), Karlsruher Institut für Technologie (KIT)


We address the problem of determining convergent upper bounds in continuous non-convex global minimization of box-constrained problems with equality constraints. These upper bounds are important for the termination of spatial branch-and-bound algorithms. Our method is based on the theorem of Miranda which helps to ensure the existence of feasible points in certain boxes. Then, the computation of upper bounds at the objective function over those boxes yields an upper bound for the globally minimal value. A proof of convergence is given under mild assumptions. An extension of our approach to problems including inequality constraints is possible.

Verlagsausgabe §
DOI: 10.5445/IR/1000118520
Veröffentlicht am 20.04.2020
DOI: 10.1007/s10107-020-01493-2
Zitationen: 1
Web of Science
Zitationen: 1
Zitationen: 1
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Operations Research (IOR)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2021
Sprache Englisch
Identifikator ISSN: 0025-5610, 1436-4646
KITopen-ID: 1000118520
Erschienen in Mathematical programming
Verlag Springer
Band 187
Seiten 617–651
Vorab online veröffentlicht am 06.04.2020
Nachgewiesen in Dimensions
Web of Science
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