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Simulated annealing with a potential function with discontinuous gradient on Rd |
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| Authors: | GONG Guanglu LIU Yong QIAN Minping |
| Institution: | 1. Department of Probability and Statistics, Peking University, Beijing 100871, China;Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China 2. Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100080 , China 3. Department of Probability and Statistics, Peking University, Beijing 100871, China |
| Abstract: | In this paper, we have proven that the simulated annealing processdX t = −β(t) ∇U (X t ) + √2dW tt 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. |
| Keywords: | simulated annealing self-organizing algorithm of Kohonen log-Sobolev inequality estimate of spectral gap |
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