Simulated Annealing Type Algorithms for Multivariate Optimization
MASSACHUSETTS INST OF TECH CAMBRIDGE LAB FOR INFORMATION AND DECISION SYSTEMS
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We study the convergence of a class of discrete-time continuous-state stimulated annealing type algorithms for multivariate optimization. The general algorithm that we consider is of the form Xk1 Xk - akdelUXk xik bkWk. Here U. is a smooth function on a compact subset of real number r, xik is a sequence of real number r - valued random variables, Wk is a sequence of independent standard r-dimensional Gaussian random variables, and ak, bk are sequences of positive numbers which tend to zero. These algorithms arise by adding slowly decreasing white Gaussian noise to gradient descent, random search, and stochastic approximation algorithms. We show that under suitable conditions on U., xik, ak and bk that Xk converges in probability to the set of global minima of U..
- Statistics and Probability