1 Notations 2 TD 4/10/2012

N Z R
C(·,·)
| · |
RdCdk·k
A A∗KerAImA
J
J(x) := 1
2(Ax,x)−(b,x)
A∈Mat(N, N)
J(x)

uRdA∈ Md,d(R)
J
J(u) := (Au,u)
(u,u),∀u∈Rd
u0λ0
λ0:= min
u∈RdJ(u)
u∈Rd
lim
σ→0
1
σ{J(u+σw)−J(u)}
|u| → 0
A
Ju
(J00(u)h,h)
A
A
J1(u) = u2
1
Pd
i=1 u2
i
, J2(u) = u1u2
u2
1+u2 2
,
J2A
D
λ0Id p λ0
A
A

A
0< λ0< λ1<· · · < λn
λivi
Vi:= Span{v1,...,vi−1}⊥,∀i≥1
w∈Vi
∀j∈ {1, . . . , i −1}(w,vi)≡0
∀w∈Vi, J(w)≥λi
L(u, λ)=(Au,u)−λ{(u,u)−1}
∂uL= 0, ∂λL= 0.
(x, y)c(x, y)
(x, y)∈R2(x0, y0) (x1, y1)
y(x)
y:= y(x)
y

c(x, y) = (c1, x ≥0,
c2, x < 0.