Multiple Peano Scannings and Multidimensional Problems

  • Roman G. Strongin
  • Yaroslav D. Sergeyev
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 45)


We commence by recalling some properties of the Peano curve y(x) from Theorem 8.1. From (8.1.21)–(8.1.23) follows that any two points x′, x″ from the unit interval [0,1] on the x-axis have some close images y′ = y(x′), y″ = y(x″) in the hypercube
; herewith, if
$$ \left| {x' - x''} \right| \leqslant {2^{ - \left( {M + 1} \right)N,}} $$
, where M ≥ 1 is an integer, then
$$ \max \left\{ {\left| {{{y'}_j} - {{y''}_j}} \right|:1 \leqslant j \leqslant N} \right\} \leqslant {2^{ - M}}. $$


Global Optimization Interior Point Limit Point Inverse Image Common Vertex 
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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Roman G. Strongin
    • 1
  • Yaroslav D. Sergeyev
    • 1
    • 2
  1. 1.Nizhni Novgorod State UniversityNizhni NovgorodRussia
  2. 2.Institute of Systems Analysis and Information TechnologyUniversity of CalabriaRendeItaly

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