Space filling curves and mathematical programming

摘要: The problem of finding {if314-1} in n dimensional Euclidean space such that {if314-2}, i = 1, 2, ···, N , is considered. only assumption on the f a solution exists quantized unit hypercube. Implicitly exhaustive procedures, which obtain solutions by implicitly considering every point without making computations at each point, are studied. feature made possible adapting “space filling curves≓ to discrete spaces general dimensionality. Several curves surveyed, and Peano's continuous mapping from interval onto square used as basis for defining hypercube, inversely. Ternary arithmetic required functional relationships mapping. has attributes quasi-continuity, specific numerical bounds derived this respect. It shown these optimal order dependence relevant variables. how use knowledge first second properties digital computer using concept search. global assumed first, or possibly second, variations. Concluding remarks bear ultimate practicality method, present limited amount experimental data.