We suggest an approach to solve special classes of multi-extreme problems to optimize the combination (e.g., sum, product) of several functions, under the assumption that the effective algorithms to optimize each of this item are known. The algorithm proposed is iterative. It realizes one of the idea of the branch-and-bound method and consists in successive correcting of the low and the upper bounds of optimal value of objective functions. In each iteration, the total area of the considered region that may contain the image optimal point, decreases at least twice. Various techniques that accelerate the process of finding solutions are discussed.