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Simulated annealing with time-dependent energy function. (English) Zbl 0790.90058
We consider, in a general algebraic framework, a class of time- inhomogeneous evolutions which reduce to a variant (with time-dependent energy function) of the well-known simulated annealing algorithm when the algebra \(\mathcal M\) involved is \({\mathcal L}^ \infty(X)\), \(X\) being a finite set or the \(d\)-dimensional torus. We compare the time evolved \(\varphi_ n\) of an arbitrary initial state \(\varphi_ 0\) on \(\mathcal M\) with the instantaneous equilibrium state \(\mu_ n\) of the inhomogeneous evolution, and we prove asymptotic indistinguishability of the two under suitable conditions.

90C27 Combinatorial optimization
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