Optimization and Tropical Geometry

This is a BMS Advanced Course which is part of the Thematic Einstein Semester Network Games, Tropical Geometry and Quantum Communication. The course takes place on Mondays, 10-12, in MA 041 at TU Berlin.

Teaching assistant: Robert Löwe

Contents

  1. Shortest Paths and the Hungarian Method [15 April]; notes and exercises/problems
  2. Tropical Hypersurfaces [29 April]; notes and exercises/problems
  3. Tropical Linear Programming, MEAN-PAYOFF and Semi-Algebraic Sets [06 May]; notes and exercises/problems
  4. Product-Mix Auctions [13 May]; notes, ipynb for polymake 3.4 and exercises/problems
  5. Multicriteria Optimization and Alexander Duality of Monomial Ideals [20 May]; notes and exercises/problems
  6. Divisors on Curves, Riemann-Roch and Chip Firing Games [27 May]; notes and exercises/problems

This course will be followed by an international conference (hosted at ZIB in June) and subsequent project work. For each lecture I will provide a set of problems that the participants are expected to work on, on their own. The final jour fixe before the projects start (on Wednesday, 29 May, 10:15 in MA 315 at TU) provides an excellent opportunity for exchange on those problems and to ask questions.

Participants of the TES are expected to work on projects to be presented at the final workshop on 1 July (hosted at ZIB).

The Kickoff Meeting took place on 09 April, 18:00 at Mathematische Fachbibliothek, TU Berlin.

References

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Allamigeon, Xavier, Pascal Benchimol, Stéphane Gaubert, and Michael Joswig. 2014. “Combinatorial Simplex Algorithms Can Solve Mean Payoff Games.” SIAM J. Opt. 24 (4): 2096–2117. doi:10.1137/140953800.

———. 2015. “Tropicalizing the Simplex Algorithm.” SIAM J. Discrete Math. 29 (2): 751–95. doi:10.1137/130936464.

———. 2018. “Log-Barrier Interior Point Methods Are Not Strongly Polynomial.” SIAM J. Appl. Algebra Geom. 2 (1): 140–78. doi:10.1137/17M1142132.

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Last modified: Son Sep 15 09:09:49 UTC 2019 by mic