| Simulated Annealing Type Algorithms for Multivariate Optimization (2007) | |||||||||||
Abstract | |||||||||||
| 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 Xk+1= Xk - a(k)(delU(Xk) + 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(.).. Prepared in cooperation with Computer Vision and Image Processing Laboratory, School of Electrical Engineering, Purdue University, West Lafayette, IN. | |||||||||||
Publication details | |||||||||||
| |||||||||||