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Abstract: In this paper, we give new results on the Alienor method of dimension reduction. This technique is used to solve multidimensional global optimization problems of type min x∈X f(x) where f is a non convex Lipschitz function and X a compact set of defined by Lipschitz constraints. The idea is to construct an α-dense curve h in the feasible set X. The global minimum of f on X is then approximated by the global minimum of f on the curve h. That is, our problem has become a one-dimensional problem which can be solved by the Piyavskii–Shubert method. Examples of these curves and numerical implementations on several test functions are given. [Copyright &y& Elsevier]