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f, G :R27→ RC1
min
G(x)=0f(x).
f:Rn7→ RG:Rn7→ Rm
min
G(x)=0f(x).
min
x+3y=1(2x2+ 3y4),
min
x2+4y2=1(xey),
min
x2−y−z=1(ex4+y4+z4),
(x1, x2, x3, x4)∈(R∗
+)4,min
x1x2x3x4=1(x1+x2+x3+x4).
G(x, y, z)=(z−x2−y2, z +x4+y4),min
G=(−1,2)(x2+y2+z4),
G(x1, x2, y1, y2)=(x2
1+x2 2, y2 1+y2 2),max
G=(1,1)(x1y1+x2y2),
G(x, y, z, w) = (x+y+z+w, x2+y2+z2+w2, x3+y3+z3+w3),min
G=(1,2,3)x4+y4+z4+w4.

(v1, v2, v3)∈R3f(v1, v2, v3) = det(v1, v2, v3)G(v1, v2, v3)=(||v1||,||v2||,||v3||)
f{(v1, v2, v3) : G(v1, v2, v3) = (1,1,1)}
G(v1, v2, v3) (v1, v2, v3)
|det(v1, v2, v3)| ≤ ||v1|| ||v2|| ||v3||.