Interval Algorithm For Multi-Minimum Optimization Over Bounded Domains

Interval mathematics is a generalization of real mathematics. The concept of the theory is that, instead of operating with real numbers of a variable x. all operations are performance by the interval that contains x.In recent years, interval algorithm has been applied to optimization problems. They are solved by a procedure which is similar to the well-known branch and bound strategy. An interval, which contains the global optimal point, is found by dividing the design domains into small sub-boxes.Based on [2], [3], [5], [6]. and [19] . we generalize the classic bisection method to interval space, and replace interval Newton method. Thus the requirement of the objective function degenetates from C2 ro C1 and makes wide applications of the algorithm. As for the subdivision strategy( cf. [18], [25] ). we use three parameters, replace the traditional bisection with different strategies according to the objec-tive function value automatically.In this thesis, we mainly consider the following problem:global min f(x) s.t. x X0where X0 Rm is a closed interval , and f is C1 over X0.