Optimization by space‐densifying curves as a natural generalization of the Alienor method Available to Purchase

The Alienor method offers a powerful approximation technique for the optimization of continuous multivariable functions defined on a compact set H of Rⁿ. Its computational efficiency is completed by the fact that it gave rise to the theory of space‐densifying curves. Presents a survey of these curves, analysing their most important properties and characteristics. Finally, the concept of theoretic calculation time (t.c.t.) associated with each curve suggests an interesting geometric problem on the existence of a curve with minimal t.c.t.