Informatica

The optimization problems occurring in nonlinear regression normally cannot be proven unimodal. In the present paper applicability of global optimization algorithms to this problem is investigated with the focus on interval arithmetic based algorithms.

The results of experimental testing of balanced random interval arithmetic with typical mathematical test functions and practical problem are presented and discussed. The possibility of evaluation ranges of functions using balanced random interval arithmetic is investigated. The influence of the predefined probabilities of standard and inner interval operations to the ranges of functions is experimentally investigated.

In well-known statistical models of global optimization only values of objective functions are taken into consideration. However, efficient algorithms of local optimization are also based on the use of gradients of objective functions. Thus, we are interested in a possibility of the use of gradients in statistical models of multimodal functions, aiming to create productive algorithms of global optimization.

The maximization problem for an objective function f given on a feasible region X is considered, where X is a compact subset of Rⁿ and f belongs to a set of continuous multiextremal functions on X can be evaluated at any point x in X without error, and its maximum M=max x∈Xf(x) together with a maximizer x^*(a point x^* in X such that M=f(x^*)) are to be approximated. We consider a class of the global random search methods, underlying an apparatus of the mathematical statistics and generalizing the so-called branch and bound methods.

In the paper the global optimization is described from the point of an interactive software design. The interactive software that implements numeric methods and other techniques to solve global optimization problems is presented. Some problems of such a software design are formulated and discussed.