問題 #1
問題歸類
PBR-T1-1
來源
Betts
決策變量個數
n = 2 n=2 n=2
限制個數
m 1 = 0 , m − m 1 = 0 , b = 1 m_1=0,m-m_1=0,b=1 m1=0,m−m1=0,b=1
目标函數
f ( x ) = 100 ( x 2 − x 1 2 ) 2 + ( 1 − x 1 ) 2 f(x)=100(x_2-x_1^2)^2+(1-x_1)^2 f(x)=100(x2−x12)2+(1−x1)2
限制條件
− 1.5 ≤ x 2 -1.5\le x_2 −1.5≤x2
起始點
x 0 = ( − 2 , 1 ) ( f e a s i b l e ) \bm{x}_0=(-2,1) \qquad (feasible) x0=(−2,1)(feasible)
f ( x 0 ) = 909 f(\bm{x}_0)=909 f(x0)=909
結果
x ∗ = ( 1 , 1 ) \bm{x}^*=(1,1) x∗=(1,1)
f ( x ∗ ) = 0 f(\bm{x}^*) = 0 f(x∗)=0
r ( x ∗ ) = 0 r(\bm{x}^*) =0 r(x∗)=0