Optimization in Multi-Agent Systems

All materials, such as lecture slides, exercise sheets and sample solutions are available for download in Moodle. The lecture and the exercise take place every week and last two lecture and exercise units respectively.

This is a '2+1' course, which consists of a lecture part and an exercise part. The lecture is held by Dr.rer.nat. Tatiana Tatarenko in the sommer semester.

The language of the lecture is English:

Part I: Preliminaries

• Unconstrained optimization: necessary and sufficient conditions of extremum;
  • Unconstrained optimization problem: existence, uniqueness, stability;
  • Gradient descent in convex optimization, its convergence.

• Constrained optimization: Karush-Kuhn-Tucker condition;
  • Optimization subjected to convex simple constraints;
  • Gradient projection method and its convergence properties;
  • Optimization subjected to inequality constraints;

Part II: Game-theoretic Optimization

• Background of game theory: Nash equilibrium concept, finite action games, examples;
• Potential games;
• Continuous action games with convex cost functions;
• Variational inequalities, their connection to Nash equilibria in convex games;
• Existence and uniqueness of Nash equilibrium in convex games;
• Gradient methods and their behavior in convex games;
• Information settings in systems: communication- and payoff-based methods;
• Modern applications and their challenges.

Part III: Distributed Optimization

• Motivating examples; interaction through communication;
• Consensus in MAS;
• Unconstrained/constrained distributed optimization;
• Modern applications and their challenges.