Generalized Subinterval Selection Criteria for Interval Global Optimization

Abstract

The convergence properties of interval global optimization algorithms are studied which select the next subinterval to be subdivided with the largest value of the indicator pf(f k ,X)=(f k −\(\underline F \)(X))/(\(\overline F \)(X)−\(\underline F \)(X)). This time the more general case is investigated, when the global minimum value is unknown, and thus its estimation f k in the iteration k has an important role. A sharp necessary and sufficient condition is given on the f k values approximating the global minimum value that ensure convergence of the optimization algorithm. The new theoretical result enables new, more efficient implementations that utilize the advantages of the pf* based interval selection rule, even for the more general case when no reliable estimation of the global minimum value is available.