第3章 無約束最優(yōu)化方法 3-1 最速下降法 3-2 牛頓法

1、)( kkk xfHd IH k )( 2 kk xfH n Rx 0 )(xf)(xfxx * )(xfd )(min 0 dxf xdx n 1 0 x 2 1 1 1 2 )( 4 )( )( n n TT T xGxGxx xx Gxxxf T 2 1 )(min 1 n * x )()( )( )( ) 1( ) 1( )()( * 2 1 2 1 2 2 * 1 xfxfxfxf k n n k * 2 1 11 2 2 * 1 )1( )1( xxxx k n n n k xbGxxxf TT 2 1 )( 0 k Mdxf kkk )( 2 0 )(,cos)( 2 1 )()

2、( 2 2 kkkkkkk xfdxf M dxfxf k x * x )(xf * x 0)( * xf)( *2 xf )( k xf )( * xf 1 )()( )()( * * 1 k k k xfxf xfxf 1suplim M mM k k Mm n 1 0 n 1 )( 2 xf )(xf * xk x )(xf )(xf * x 1k x 1k x )(xf * x )(xf)(xf k x )()( 2 1 )()()()()( 2 kk T kk T kkk xxxfxxxxxfxfxqxf 0)()()( 2 kkkk xxxfxfxq )()( 2 kkk xfxx

3、xf )( 2 k xf 12 )( k xf )()( 12 1kkkk xfxfxx )()( 2 kkk xfxfd )(xf * x)(xf 0)( * xf)( 2 k xf )( 2 xf 0 n jiji Ryxyxyfxf,)()( ),( 2 ),( 2 ),( 2 )( ji xf )( 2 xfji, 0 x * x * x k x 0 x * x )()( 12 1kkkkkkkk xfxfxdxx )(xf Dx 0 0m )(xf)()(|)( 00 xfxfxxL nT Ruumuxfu 2 2 )( 0 x k x )(xf k x )(xf )(xf Dx 0

4、 0m )(xf)()(|)( 00 xfxfxxL nT Ruumuxfu 2 2 )( 0 x k x0)(lim k k xf )(xf 2 221 4 1 )1 (minxxxx T x0 , 0 0 T xf2 , 0)( 0 21 10 )( 0 2 xf )( 0 2 xf 01 12 )( 1 0 2 xf Txfxfd0 , 2)()( 0 1 0 2 0 1)2()( 4 00 dxf 0 )( sin )(),()(cos )()( 12 12 k kkk kk k xf xfxfxf xfxf d T LDL )(xf )( 2 xf Dx 0)( 2 dxfd T d

5、 0)(dxf T 0)(dxf T 0)(dxf T d d )( 2 xf k x T LDL )( k xf njed jjjj , 2 , 1, nj jt , 2 , 1|min 0 t t T k edL k x k d kk T kkkk ExfLDLG)( 2 )( 2 k xf T LDL k d t T k edL k d k x k d k dk x 0 x01k )( k xf)( 2 k xf )( 2 k xf )( k xf T LDL kk T kkk ExfLDL)( 2 )( kk T kkk xfdLDL k d njed jjjt , 2 , 1|min

6、 0 t k d t T k edL elsed xfdd d k k T kk k 0)( k d k kkkk dxx 1 )()( 1kk xfxf 1kk 0 x00k )( k xf)( 2 k xf )( 2 k xf )( k xf T LDL kk T kkk ExfLDL)( 2 )( kk T kkk xfdLDL k d njed jjjt , 2 , 1|min 0 t k d t T k edL elsed xfdd d k k T kk k 0)( k d k kkkk dxx 1 )()( 1kk xfxf 1kk k xx * )(xf n Rx )()(|)(

7、xfxfxxL 0 )( 0 xLx k x k x k x )(xf )(xf k h kk n k hxxRx| sGssxfxfsq k TT kkk 2 1 )()()( )(sxf k k k TT kkk hsts sGssxfxfxq . . 2 1 )()()(min )()( kkkk sxfxff kk T kk T kkkkk sGssxfsqxfq 2 1 )()()( k k k q f r 0 x 0 h 0 1 , 0, 21 10 21 , 1,1 , 0 21 k0 )( k xf )( k xf k xx * k G k s )( kk sxf k r 1 k r kk hh 11 2 k r kk hs kk hh 21 kk hh 1 0 k r kk xx 1 kkk sxx 1 1 kk 121 2 2 2 1 2 2 1 2 3 )(minxxxxxxf T x4 , 2