Slide 10
Slide 10 text
ࣹӨ (projection) Farkas ͷิ (Farkas’ lemma) ತؔ (convex function)
ਲ਼ͷఆٛ
ఆٛ: ਲ਼
࣍ͷ݅Λຬ͢Δू߹ C ∈ Rn Λਲ਼(cone) ͱ͍͏ɽ
x ∈ C, α ∈ [0, ∞) ⇒ αx ∈ C
ಛʹɼਲ਼͕ತू߹Ͱ͋Δͱ͖ತਲ਼ɼดू߹Ͱ͋Δͱ͖ดਲ਼ͱ͍͍ɼ
ดू߹Ͱ͋ΔΑ͏ͳತਲ਼Λดತਲ਼ͱ͍͏ɽ
ྫ 2.7
࣍ͷू߹ Ci (i = 1, 2, 3, 4) ͍ͣΕดತਲ਼Ͱ͋Δɽ
• C1 =
{
x ∈ Rn | x =
∑
m
i=1
αiai, αi
≧ 0 (i = 1, . . . , m)
}
• C2 =
{
x ∈ Rn |
⟨
ai, x
⟩
≦ 0 (i = 1, . . . , m)
}
• C3 =
{
x ∈ Rn | x2
1
≧ x2
2
+ · · · + x2
n
, x1
≧ 0
}
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