Global optimisation of constrained non-convex programs using reformulationand interval analysis

In this paper the interval global optimisation approach is recast, by refor mulation of the global optimisation problem, as a bound constrained linear relaxation, Two new classes of linear under-estimator, derived from the nat ural extension and mean value forms of interval analysis, respectively, and applicable to any once differentiable function, are introduced. These unde r-estimators are combined with the interval bounded linear program to creat e a rigorous global optimisation algorithm for constrained global optimisat ion. The value of the approach is validated by application to selected test problems from the process engineering and global optimisation literature. The results indicate that the interval LP is more efficient than other inte rval methods for constrained problems whilst retaining a wide applicability . (C) 1999 Elsevier Science Ltd. All rights reserved.