优化问题-非线性规划-problem1

问题 #1

问题归类

PBR-T1-1

来源

Betts

决策变量个数

n = 2 n=2 n=2

约束个数

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

目标函数

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

约束条件

− 1.5 ≤ x 2 -1.5\le x_2 −1.5≤x2​

起始点

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

结果

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