Abstract
Global optimization of multiextremal functions of several variables, i.e., functions possessing multiple local extrema, remains one of the most challenging problems in computational mathematics.The importance of this problem stems from its widespread occurrence in both theoretical research and practical applications.In previous work by one of the authors, a special transformation of the original objective function was proposed to construct an auxiliary function.Several key properties of this auxiliary function, including non-negativity, uniform continuity, differentiability, and monotonicity, were rigorously established.These properties ensure computational efficiency and provide theoretical guarantees of convergence for the proposed global optimization method.In this paper, necessary and sufficient conditions for the existence of a global minimum of the objective function are derived and proved.As a result, the original optimization problem is reduced to finding the greatest zero of a convex univariate function.It is shown that the global minimum of the objective function coincides with the supremum of the set of zeros of the auxiliary function.This characterization enables the use of well-established numerical methods to compute the greatest zero with high accuracy.