Solution of special classes of multi-extremal problems

We suggest an approach to solve special classes of multi-extremal problems to optimize the monotone combination (e.g., sum, product) of several functions, under the assumption that the effective algorithms to optimize each of this item are known (e.g., each of these functions has some properties of generalized concavity: linear fractional, etc.) The algorithm proposed is iterative. It realizes one of the idea of the branchand- bound method and consists in successive correcting of the low and the upper bounds of optimal value of objective functions. Moreover, we use the methodology of multi-objective optimization, studying the image of Pareto boundary in the image space. In each iteration, the total area of the region, guaranteed to contain the image optimal point, decreases at least twice.