Diffusions for Global Optimization
- 1 July 1986
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Control and Optimization
- Vol. 24 (5) , 1031-1043
- https://doi.org/10.1137/0324060
Abstract
We seek a global minimum of U:(0, 1)"-. R. The solution to (d/dt)x,=-VU(xt) will find local minima. The solution to dxt =-V U(xt) dt+ dw,, where w is standard (n-dimensional) Brownian motion and the boundaries are reflecting, will concentrate near the global minima of U, at least when "temperature" T is small: the equilibrium distribution for xt is Gibbs with density 'r(x)a exp {-U(x)/T}. This suggests setting T T(t)0 to find the global minima of U. We give conditions on U(x) and T(t) such that the solution to dxt=-V U(xt)dt+x/ dw converges weakly to a distribution concentrated on the global minima of U.Keywords
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