GLOBAL CONSTRAINED OPTIMIZATION USING INTERVAL ANALYSIS

Publisher Summary This chapter discusses the global constrained optimization using interval analysis. It also presents an algorithm for computing the global unconstrained minimum of a function f:R n → R. The algorithm is extended to the case in which the minimum is subject to inequality constraints. The algorithm provides both upper and lower bounds of f and on each of the components of x . As the search is exhaustive and as errors are bound using interval analysis, there is no question but that the bounds are correct. Their sharpness improves as the algorithm proceeds. The only question is whether the desired sharpness can be obtained with a reasonable amount of computing. It would certainly be possible to derive examples on which the algorithm is prohibitively slow. However, the algorithm will solve the case in which both the objective function f and the constraint functions p i (i = 1 , … , m ) are nonlinear.