کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1156513 958836 2008 44 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Annealing diffusions in a potential function with a slow growth
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Annealing diffusions in a potential function with a slow growth
چکیده انگلیسی

Consider a continuous analogue of the simulated annealing algorithm in RdRd, namely the solution of the SDE dXt=σ(t)dBt−∇V(Xt)dt, where VV is a function called the potential. We prove a convergence result, similar to the one in [L. Miclo, Thèse de doctorat, Ph.D. Thesis, Université Paris VI, 1991], under weaker hypotheses on the potential function. In particular, we cover cases where the gradient of the potential goes to zero at infinity. The main idea is to replace the Poincaré and log-Sobolev inequalities used in [L. Miclo, Thèse de doctorat, Ph.D. Thesis, Université Paris VI, 1991; C.-R. Hwang, T.-S. Chiang, S.-J. Sheu, Diffusion for global optimization in Rn, SIAM J. Control Optim. 25 (1987) 737–753.] by the weak Poincaré inequalities (introduced in [M. Röckner, F.-Y. Wang, Weak Poincaré inequalities and L2L2 convergence rates of Markov semigroups, J. Funct. Anal. 185 (2001) 564–603]), and to estimate constants with measure–capacity criteria. We show that the convergence still holds for the ‘classical’ schedule σ(t)=c/ln(t)σ(t)=c/ln(t), where cc is bigger than a constant related to VV (namely the height of the largest potential barrier).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 118, Issue 1, January 2008, Pages 76–119
نویسندگان
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