Abstract
Original language | English |
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Place of Publication | Tilburg |
Publisher | Operations research |
Number of pages | 13 |
Volume | 2005-125 |
Publication status | Published - 2005 |
Publication series
Name | CentER Discussion Paper |
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Volume | 2005-125 |
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Keywords
- global optimization
- standard simplex
- PTAS
- multivariate Bernstein approximation
- semidefinite programming
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On the Complexity of Optimization over the Standard Simplex. / de Klerk, E.; den Hertog, D.; Elfadul, G.E.E.
Tilburg : Operations research, 2005. (CentER Discussion Paper; Vol. 2005-125).Research output: Working paper › Discussion paper › Other research output
TY - UNPB
T1 - On the Complexity of Optimization over the Standard Simplex
AU - de Klerk, E.
AU - den Hertog, D.
AU - Elfadul, G.E.E.
N1 - Subsequently published in the European Journal of Operational Research, 2008 Pagination: 13
PY - 2005
Y1 - 2005
N2 - We review complexity results for minimizing polynomials over the standard simplex and unit hypercube.In addition, we show that there exists a polynomial time approximation scheme (PTAS) for minimizing Lipschitz continuous functions and functions with uniformly bounded Hessians over the standard simplex.This extends an earlier result by De Klerk, Laurent and Parrilo [A PTAS for the minimization of polynomials of fixed degree over the simplex, Theoretical Computer Science, to appear.]
AB - We review complexity results for minimizing polynomials over the standard simplex and unit hypercube.In addition, we show that there exists a polynomial time approximation scheme (PTAS) for minimizing Lipschitz continuous functions and functions with uniformly bounded Hessians over the standard simplex.This extends an earlier result by De Klerk, Laurent and Parrilo [A PTAS for the minimization of polynomials of fixed degree over the simplex, Theoretical Computer Science, to appear.]
KW - global optimization
KW - standard simplex
KW - PTAS
KW - multivariate Bernstein approximation
KW - semidefinite programming
M3 - Discussion paper
VL - 2005-125
T3 - CentER Discussion Paper
BT - On the Complexity of Optimization over the Standard Simplex
PB - Operations research
CY - Tilburg
ER -