BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Johan Karlsson (KTH) DTSTART:20241125T121500Z DTEND:20241125T130000Z DTSTAMP:20260417T003635Z UID:cam/44 DESCRIPTION:Title: Str uctured multi-marginal optimal transport: Applications\, theory\, and comp utations\nby Johan Karlsson (KTH) as part of CAM seminar\n\nLecture he ld in MV:L14.\n\nAbstract\nThe optimal mass transport problem is a classic al problem in mathematics\, and dates back to 1781 and work by G. Monge wh ere he formulated an optimization problem for minimizing the cost of trans porting soil for construction of forts and roads. Historically the optimal mass transport problem has been widely used in economics in\, e.g.\, plan ning 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 deve lopment of theory and methods for optimal mass transport and the ideas hav e attracted considerable attention in several economic and engineering fie lds. These developments have led to a mature framework for optimal mass tr ansport with computationally efficient algorithms that can be used to addr ess many problems in applied mathematics.\n\n \n\nIn this talk\, I will gi ve 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 con trol and estimation of multi-agent systems. This the optimal transport fra mework allows for replacing the standard state space formalist\, where a s tate evolve over time\, to a setting where instead densities or multi-agen t systems evolve over time. In this setting we can formulate and solve a l arge set of problems\, e.g.\, with given dynamics of the underlying agents and multiple classes of agents\, nonlocal interactions\, or include const raints between different time points such as origin destination constraint s. We will also consider computational methods\, and motivated by Sinkhorn 's method for the standard optimal transport problems\, it can be shown th at dual coordinate ascent is a computationally efficient approach for this class of problems. \n\nIn this talk\, I will give an overview of the mult i-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 mul ti-agent systems. This the optimal transport framework allows for replacin g 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 a gents\, nonlocal interactions\, or include constraints between different t ime points such as origin destination constraints. We will also consider c omputational 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.\n LOCATION:https://researchseminars.org/talk/cam/44/ END:VEVENT END:VCALENDAR