Computational and Applied Mathematics seminar

Abstrakt finns enbart på engelska: The optimal mass transport problem is a classical problem in mathematics, and dates back to 1781 and work by G. Monge where he formulated an optimization problem for minimizing the cost of transporting soil for construction of forts and roads. Historically the optimal mass transport problem has been widely used in economics in, e.g., planning and logistics, and was at the heart of the 1975 Nobel Memorial Prize in Economic Sciences. In the last two decades there has been a rapid development of theory and methods for optimal mass transport and the ideas have attracted considerable attention in several economic and engineering fields. These developments have led to a mature framework for optimal mass transport with computationally efficient algorithms that can be used to address many problems in applied mathematics.

In this talk, I will give an overview of the multi-marginal optimal mass transport framework and show how it can be applied to address and solve a range of problems in control and estimation of multi-agent systems. This the optimal transport framework allows for replacing the standard state space formalist, where a state evolve over time, to a setting where instead densities or multi-agent systems evolve over time. In this setting we can formulate and solve a large set of problems, e.g., with given dynamics of the underlying agents and multiple classes of agents, nonlocal interactions, or include constraints between different time points such as origin destination constraints. We will also consider computational methods, and motivated by Sinkhorn's method for the standard optimal transport problems, it can be shown that dual coordinate ascent is a computationally efficient approach for this class of problems.

In this talk, I will give an overview of the multi-marginal optimal mass transport framework and show how it can be applied to address and solve a range of problems in control and estimation of multi-agent systems. This the optimal transport framework allows for replacing the standard state space formalist, where a state evolve over time, to a setting where instead densities or multi-agent systems evolve over time. In this setting we can formulate and solve a large set of problems, e.g., with given dynamics of the underlying agents and multiple classes of agents, nonlocal interactions, or include constraints between different time points such as origin destination constraints. We will also consider computational methods, and motivated by Sinkhorn's method for the standard optimal transport problems, it can be shown that dual coordinate ascent is a computationally efficient approach for this class of problems.