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SUMMARY:Interacting Particle Systems: Fast algorithms and non-convex o
 ptimization (Jin\, Shanghai Jiao Tong University)
UID:982527f6-9dbf-4424-9a5d-794d8926603c
DESCRIPTION:Interacting Particle Systems: Fast algorithms and non-conv
 ex optimization Speaker: Prof. Dr. Shi Jin Affiliation: Shanghai Jiao 
 Tong University Abstract: We first develop random batch methods for cl
 assical and quantum interacting particle systems with large number of 
 particles. These methods use small but random batches for particle int
 eractions\, thus the computational cost is reduced from O(N^2) per tim
 e step to O(N)\, for a system with N particles with binary interaction
 s. For classical particles we give a particle number independent error
  estimate under some special interactions. For quantum N-body Schrodin
 ger equation\, we obtain\, for pair-wise random interactions\, a conve
 rgence estimate for the Wigner transform of the single-particle reduce
 d density matrix of the particle system at time t that is uniform in N
  > 1 and independent of the Planck constant hbar. We then introduce a 
 stochastic interacting particle consensus system for global optimizati
 on of high dimensional non-convex functions. This algorithm does not u
 se gradient of the function thus is suitable for non-smooth functions.
  We prove that under dimension-independent conditions on the parameter
 s and with suitable initial data the algorithms converge to the neighb
 orhood of the global minimum almost surely. Applied Analysis
DTSTART:20200624T100000Z
DTEND:20200624T110000Z
LOCATION:Online (contact marius.yamakou@fau to get the data for the VC)
DTSTAMP:20260731T094046Z
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