Convergence with Hilbert's space filling curve

摘要

The subject of this paper is a means of converging to a set of numbers in certain mathematical programming problems where a conventional programming method is not possible. The space filling curve is shown to provide a tool for doing this. An algorithm for generating such a curve is presented; the resulting space filling curve is a generalization of a mapping which Hilbert gave for the unit square only, in geometric form only. The following topics are discussed: convergence to solutions of systems of equalities or inequalities, convergence to minima, the advantages of the present space filling curve over other known space filling curves, some experimental results, and the relation between these methods and the standard methods of mathematical programming.