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On the complexity of optimization over the standard simplex


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  • de Klerk, E.
  • den Hertog, D.
  • Elabwabi, G.


We review complexity results for minimizing polynomials over the standard simplex and unit hypercube. In addition, we derive new results on the computational complexity of approximating the minimum of some classes of functions (including Lipschitz continuous functions) on the standard simplex. The main tools used in the analysis are Bernstein approximation and Lagrange interpolation on the simplex combined with an earlier result by de Klerk et al. [A PTAS for the minimization of polynomials of fixed degree over the simplex, Theoretical Computer Science 361 (2-3) (2006) 210-225].

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Bibliographic Info

Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 191 (2008)
Issue (Month): 3 (December)
Pages: 773-785

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Handle: RePEc:eee:ejores:v:191:y:2008:i:3:p:773-785

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Cited by:
  1. Immanuel Bomze & Stefan Gollowitzer & E. Yıldırım, 2014. "Rounding on the standard simplex: regular grids for global optimization," Journal of Global Optimization, Springer, vol. 59(2), pages 243-258, July.
  2. Klerk, E. de, 2006. "The Complexity of Optimizing over a Simplex, Hypercube or Sphere: A Short Survey," Discussion Paper 2006-85, Tilburg University, Center for Economic Research.


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