最优化理论与算法(20)

= 2f(x(0)) 1( f(x(0)) f(x ) 2f(x(0))(x(0) x )) ≤M f(x(0)) f(x ) 2f(x(0))(x(0) x )

1

≤M 2f(x +t(x(0) x )) 2f(x(0)) x(0) x dt≤M+≤

01

1

2f(x +t(x(0) x )) 2f(x ) x(0) x dt

(0)

f(x

2

) f(x) x

2 (0)

x dt

1(0)

x x .2

(3.4.2)

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x(k+1) x ≤

l §{x(k)}Âñux "? Ú§ k¿© § x

(k+1)

1(k)

x x .2

x ≤M

1

2f(x +t(x(k) x )) 2f(x(k)) x(k) x dt=o( x(k) x ),

={x(k)} 5Âñux "

e 2f3x ?LipschitzëY§K

1

x(k+1) x ≤M 2f(x +t(x(k) x )) 2f(x ) x(k) x dt

+

001

f(x

01

2(k)

) f(x) x

2 (k)

x dt

≤LM=

={x(k)} gÂñux "

tdt+1 x(k) x 2

3

LM x(k) x 2,2

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