Simulated annealing with a potential function with discontinuous gradient on Rd

• Published in: Science China. Mathematics Vol. 44; no. 5; pp. 571 - 578
• Main Authors: Gong, Guanglu, Liu, Yong, Qian, Minping
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 01.05.2001; Department of Probability and Statistics, Peking University, Beijing 100871, China; Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China%Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100080 , China%Department of Probability and Statistics, Peking University, Beijing 100871, China
• Subjects: Simulated annealing; log_Sobolev inequality; estimate of spectral gap; simulated annealing; self-organizing algorithm of Kohone n
• ISSN: 1006-9283; 1674-7283; 1862-2763; 1869-1862
• DOI: 10.1007/BF02876705

In this paper, we have proven that the simulated annealing processdXt = −β(t) ∇U (Xt) + √2dWtt with a potential function on Rd, of which the gradient is discontinuous, converges in probability to a neighborhood of the global minima of the potential function.