Mathematics for Economists

Constrained positive deÖnite matrixes

Example

Solvex 1 +x 2 !min,x 12 +x 22 = 1.

The Lagrangian is

L(x 1 ,x 2 ,λ)=x 1 +x 2 +λ

x 12 +x 22  1

.

The necessary conditions

1 + 2 λx 1 = 0 , 1 + 2 λx 2 = 0 ,)x 1 =x 2 , 2 x 12 = 1 ,x 1 = 1 /

p

2.