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Leitung

Prof. Dr. Peter Bürgisser

Lupe

Anschrift
Technische Universität Berlin
Institut für Mathematik
Sekretariat MA 3-2
Straße des 17. Juni 136
10623 Berlin

Büro
Raum MA 317 (3. OG)
Institut für Mathematik

Kontakt

Sekretariat
Beate Nießen
Raum MA 318
Tel.: +49 (0)30 314 - 25771

eMail
peter.buergisser@offmath.tu-berlin.de

Telefon
+49 (0)30 314 - 75902
Faxgerät
+49 (0)30 314 - 25839

Sprechstunde
Während der Vorlesungszeit: Do, 15-16 Uhr.
Während der vorlesungsfreien Zeit: nach Vereinbarung.

Publikationen

Interior-point methods for unconstrained geometric programming and scaling problems
Citation key BLNW-Interior-Point-Methods-for-unconstrained-Geometric-Programming
Author Peter Bürgisser and Yinan Li and Harold Nieuwboer and Michael Walter
Year 2020
Abstract We provide a condition-based analysis of two interior-point methods for unconstrained geometric programs, a class of convex programs that arise naturally in applications including matrix scaling, matrix balancing, and entropy maximization. Our condition numbers are natural geometric quantities associated with the Newton polytope of the geometric program, and lead to diameter bounds on approximate minimizers. We also provide effective bounds on the condition numbers both in general and under combinatorial assumptions on the Newton polytope. In this way, we generalize the iteration complexity of recent interior-point methods for matrix scaling and matrix balancing. Recently, there has been much work on algorithms for certain optimization problems on Lie groups, known as capacity and scaling problems. For commutative groups, these problems reduce to unconstrained geometric programs, which serves as a particular source of motivation for our work.
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