www-ai.cs.tu-dortmund.de/LEHRE/FACHPROJEKT/SS14/Papers/libsvm.pdf
byi
{ ≥ 0 if αi < C,
≤ 0 if αi > 0. (23)
Define
r1 ≡ ρ− b and r2 ≡ ρ+ b. (24)
If yi = 1, (23) becomes
∇if(α)− r1
{ ≥ 0 if αi < C,
≤ 0 if αi > 0. (25)
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if yi = −1, (23) becomes
∇if(α)− r2
{ ≥ 0 if αi < [...] to yi(w Tφ(xi) + b) ≥ ρ− ξi, (4)
ξi ≥ 0, i = 1, . . . , l, ρ ≥ 0.
The dual problem is
min α
1
2 αTQα
subject to 0 ≤ αi ≤ 1/l, i = 1, . . . , l, (5)
eTα ≥ ν, yTα = 0,
where Qij = yiyjK(xi,xj). Chang and [...] (wTφ(xi) + b) ≤ ε+ ξ∗i ,
ξi, ξ ∗ i ≥ 0, i = 1, . . . , l, ε ≥ 0.
The dual problem is
min α,α∗
1
2 (α−α∗)TQ(α−α∗) + zT (α−α∗)
subject to eT (α−α∗) = 0, eT (α+α∗) ≤ Cν, (10)
0 ≤ αi, α ∗ i ≤ C/l, i = 1, . . . …
