Global convergence of discrete-time inhomogeneous Markov processes from dynamical systems perspective

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• 作者：Dawid Tarłowski ; ^{dawid.tarlowski@im.uj.edu.pl} ; ^{dawid.tarlowski@gmail.com}
• 关键词：Global optimization ; Global convergence ; Inhomogeneous Markov process ; Foias operator ; Lyapunov function
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 April 2017
• 年：2017
• 卷：448
• 期：2
• 页码：1489-1512
• 全文大小：518 K
• 卷排序：448

文摘

Given the continuous real-valued objective function f   and the discrete time inhomogeneous Markov process XtXt defined by the recursive equation of the form Xt+1=Tt(Xt,Yt)Xt+1=Tt(Xt,Yt), where YtYt is an independent sequence, we target the problem of finding conditions under which the XtXt converges towards the set of global minimums of f  . Our methodology is based on the Lyapunov function technique and extends the previous results to cover the case in which the sequence f(Xt)f(Xt) is not assumed to be a supermartingale. We provide a general convergence theorem. An application example is presented: the general result is applied to the Simulated Annealing algorithm.