Minimizing Multivariable Functions by Minimization-Preserving Operators

Given a real function f of class defined on the unit cube Iⁿ=0,1]ⁿ , n ≥ 2, our purpose consists in finding an algorithm to approximate to by a dimensional reduction. The method deals with α-dense curves γ_α in the domain Iⁿ with arbitrary small density α and a minimization-preserving operator T (briefly M.P.O.) applied to the univariable function By reiterating the action of this M.P.O. we obtain an algorithm to determine a global minimizer t₀^* of f_α. The value f_α(t₀^*), taken as an approximation to f*, only depends on the density α of the curve chosen to densify the domain of the objective function.