An approximation method for the optimization of continuous functions of n variables by densifying their domains - Mora, Gaspar; Cherruault, Yves (Kybernetes, 1999)
Most of the known optimization methods for a given continuous function f defined on a compact set H = i=1,..,n[ai,bi] require strong conditions on f. In the early 1980s, Cherruault proposed a method, called ALIENOR which was able to reduce the multidimensional optimization problem to another one-dimensional optimization: the optimization of the restriction fh* of f to some adequate -dense curve h into the domain H. The characterization, the generation of such curves as well as the theoretic calculation times associated with them, have been studied previously by the authors. Their consequences and the general problem concerning the error in the approximation to global minimum of f and the minimization of the error itself, that such reduction produces, will be the subject of this paper.