Game Theory and Convex Optimization (R. Lucchetti, S. Villa)

Game theory is a very powerful tool to analyze all situations where agents interact. Its applications range from economics to psychology, from engineering to medicine. Both the non-cooperative and the cooperative theory can be profitably used. In synergy also with a group in DEIB, we consider both the theoretical and computational aspects of the theory, as well as the applications, mainly in the social sciences. Currently our research is focused in applications of Game Theory to medicine, and to Social Choice.

Convex optimization models and optimization algorithms are at the core of computational tools for inference and analysis in data sciences. Their importance has increased exceptionally in the last years, due to novel applications in signal processing, inverse problems, and machine learning. Indeed, convex optimization provides efficient algorithms converging to a global solution, with the ability of taking advantage of the geometrical structure of the sought, unknown, solution. Our research activity in this context is focused on the development of novel computational solutions, able to deal with memory, time, and communication limitations. We study convergence properties of splitting methods not only for solving minimization problems, but more generally for structured monotone inclusions in Hilbert spaces. We are in particular interested in the development of new decomposition and parallelization strategies, combined with incremental and randomized approaches, able to maintain the ability of exploiting problem structure.