An Analysis of Cut-Off Rules for Optimization Algorithms

The problem of optimal stopping has long bee of intrest to various scientific disciplines. Most notably, the approacbes taken have been based on sequential decision theory and modeling techniqes. Aiming at optimization algorithms, we propose in this paper to combine the present approaches and study the cut-off rule problem, using asymptotic convergence behavior of sequences. A unifying framework for the design and analysis of stopping rules for algorithms generating a monotonically convergent sequence is presented while methodology for optimal design is discussed. The concavity structure should be observed to play an important role in our analysis.