TopMath Spring School 2016: "Combinatorial Optimization under Uncertainty and Competition"



Venue: The TopMath Spring School 2016 will take place in the Haus der Bayrischen Landwirtschaft in Herrsching am Ammersee from 21st March – 23 rd March 2016.

Scientific Organization: T. Harks Pfeil and N. Megow

Participation: for students from the 3rd semester or higher

Bachelor`s and Master`s seminar



Combinatorial optimization is a relatively young subfield of discrete mathematics at the intersection with theoretical computer science and operations research. Intensive research in the past few decades produced powerful tools for modeling, understanding and solving combinatorial optimization problems.
A key assumption in classical problem settings is that all relevant input parameters are known in advance and all decisions are made under central control. However, uncertainty and limited control are prevalent when solving real-world problems. Uncertainty may concern parts of the problem data that is available only in probabilistic form or even unknown in advance. Consider, for example, market prices that are typically uncertain, changing customer demands, jobs that may take more or less time than originally estimated, resources that may become unavailable unexpectedly, etc. Uncertainty may also concern the strategic behavior of individual players, who held back or misrepresent data for selfish reasons and control parts of the decisions individually. This results in limited or only indirect control of decision variables in systems in which independent decision makers interact. An important example can be found in the area of network design under equilibrium constraints where network design variables are under central control while the resulting traffic distribution is governed by equilibrium conditions and, thus, only indirectly controllable.
The goal of the TopMath Spring School is to give an overview over different models, techniques, questions and performance measures for combinatorial optimization under uncertainty and competition. We study classical problems such as matching, routing, scheduling, and network design. We discuss different models of uncertainty used in the fields of online, robust and stochastic optimization. The focus will be on the design of algorithms with mathematically provable (worst-case) performance guarantees. Furthermore, we investigate optimization under limited central control, which falls in the area of computational game theory. Central challenges are the characterization of the existence and computational complexity of equilibria or stable solutions in non-cooperative and cooperative games (Nash equilibria, strong equilibria, core, nucleolus, etc.). Given an understanding of these questions is a key issue is to optimize systems having such equilibrium conditions as side constraints.
The format of the school is as follows. After introductory overview lectures by the organizers, each participant gives a talk about a preselected topic. Furthermore, we will discuss open problems in small groups.



Applications: Feel free to send your application (CV, transcript of records, short motivation statement) until 29th January 2016 to topmath@ma.tum.de


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