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Algorithmes d'optimisation sans dérivées à caractère probabiliste ou déterministe : analyse de complexité et importance en pratique

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Table 3.1: Notations for direct search with randomly generated directions.
Table 3.2: Relative performance for different sets of polling directions (n = 40). D ⊕ Q D ⊕ Q k D ⊕ 2n n + 1 n/2 n/4 2 1 arglina 3.42 8.44 16.67 10.30 6.01 3.21 1.88 1.00 – arglinb 20.50 10.35 11.38 7.38 2.81 2.35 1.85 1.00 2.04 broydn3d 4.33 6.55 11.22 6.54 3.59 2.04 1.28 1.00 – dqrtic 7.16 9.37 19.50 9.10 4.56 2.77 1.70 1.00 – engval1 10.53 20.89 23.96 11.90 6.48 3.55 2.08 1.00 2.08 freuroth 56.00 6.33 1.33 1.00 1.67 1.33 1.67 1.00 4.00 integreq 16.04 16.29 18.85 12.44 6.76 3.52 2.04 1.00 – nondquar 6.90 30.23 17.36 7.56 4.23 2.76 1.87 1.00 – sinquad – – 2.12 1.65 2.01 1.26 1.00 1.55 – vardim 1.00 3.80 3.30 1.80 2.40 2.30 1.80 1.80 4.30
Table 3.3: Relative performance for different sets of polling directions (n = 40).
Table 3.4: Relative performance for different sets of polling directions (n = 100). D ⊕ Q D ⊕ Q k D ⊕ 2 (γ = 2) 4 (γ = 1.1) arglina 1.00 3.86 105.50 5.86 7.58 arglinb 138.28 107.32 106.23 1.00 1.99 broydn3d 1.00 2.57 12.07 1.92 3.21 dqrtic 3.01 3.25 – 1.00 1.46 engval1 1.04 1.00 43.00 2.06 2.84 freuroth 31.94 17.72 12.42 1.36 1.00 integreq 1.83 1.66 13.46 1.00 1.22 nondquar 1.18 2.83 23.15 1.00 1.17 sinquad – – – – – vardim 112.22 19.72 8.04 1.00 2.36
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