algorithm simulated annealing with random walk sampler inputobjective function starting state initial temperature number of iterations nsymmetric proposal density ( )constant outputapproximate minimizer and minimum value of for to do simulate new state from the symmetric proposal ( xt if (ys (xt then xt+ else draw ( if -( ( )- (xt ))/tt then xt+ else xt+ xt + return and ( example (simulated annealing for minimizationlet us minimize the "wigglyfunction depicted in the bottom panel of figure and given by - - / sin( ) sin( ) if (xotherwise : (xe! ( )= : = ( - - - - - figure lower panelthe "wigglyfunction (xupper panelthree (normalizedgibbs pdfs for temperatures as the temperature decreasesthe gibbs pdf converges to the pdf that has all its mass concentrated at the minimizer of