1、nkRXkkkkPtXX11Rtk1kX)()(1kkXfXfkPktnkRP )(minXfnRXkXkP)(1kXf)(kkkPtXf)(kXft)()(kktPXft, 0ktt )()(1kkXfXf)0()()()(kkkkkXfPtXftkXkPkt( ) ttktkt),(PXlZs)(Xf00()min()min ( )f Xt Pf XtPtZXt P，kkkkPtXX1kXkPkkkkPtXX11kXX)(1kXf0)(1kTkPXf)()(kktPXfttkTkkPtPXft)()(0)( t0)(kTkkPtPXf0)(1kTkPXf)(minmax0ttt), 0)(

2、, 0,:max*11tttRR)(min)(max0*tttt), 0,)(, 0,maxtbaba,*bat ,ba00max0,) (0,)ttt或00h00ht )()(000tht00ht )()(000tht0tt00max0,) (0,)ttt或)(00t00h 10kkkkhtt1)(11kktkk1kkhh1ktt 1kktt1kk1kk 0k1,kkktthh11minmaxkkat tbt t，,ba211:RR 1,Rba,*bat ( ) t* ,a t( ) t* , tb,ba)(t)(t,ba,ba)(t)(t,ba,ba)(t)(t,ba 開始 選 取 初 始

3、 點0t, 初 始 步 長00h ,加步系數1,令 k=0 00( )t,比較目標函數值1kkktth,11()kkt 1min ,kat t 1max ,kbt t 結束 Y 1kkhh,ktt,1kktt, 1kk,k=k+1 N Y k=0 kkhh t=k+1 N 1kk , ,:11baRR ,21batt12tt)()(12tt,1ta)(t)()(12tt,2bt)(t圖4.3圖4.4 證明略定理4.1說明，經過函數值的比較可以把單谷區間縮短為一個較小的單谷區間換句話說利用這個定理可以把搜索區間無限縮小，從而求到極小點以下介紹的幾種一維搜索方法都是利用這個定理通過不斷地縮短搜索區

4、間的長度，來求得一維最優化問題的近似最優解min ( ) t,ba)(mintbta11RR ：,ba)(t,ba)(t,ba)(t,ba0)( t*t)(t),(*ta),(*bt*( ,)ta t0)( t0)( a),(*btt0)( t0)( b圖4.5)(t)(t,ba( )0( )0ab，,ba)(21bac0)( cca 0)( cct *0)( ccb |ba)(21*bat*tY開始確定a b ,要求c=(a+b)/2b=ct*=(a+b)/2輸出t*結束T*=cNa=cNYNY圖圖4.6 11:RR ,ba)(mintbta)(t,ba)(t,ba0)( t,bak0)(

5、tkt)(,(kktt)(ty)()(kkktttty 1kt0y)()(1kkkktttt )(t)(t,ba( )0( )0ab，0t000( )/( )tttt|0tttt 0( )tt，圖4.7)(ty,ba210ttt2t,ba 000() /()tttt 輸出*,t 開始 結束 0tt Y N 0tt *00,( )ttt 選定 t0,確定a b,要求( )0, ( )0ab 圖圖4-8 圖4.9圖4.10 xL xLxxL022LLxxLLx618. 0215圖4.11 ,ba21, tt,baab 1t,ba2t1t,ba)(618. 01abat)(382. 02abat)(

6、1t)(2t)(1t)(2t)()(21tt1t,2ta,2bt,2bt1t112, , a btb)()(21tt2t,1bt,1ta,1ta2t111, , a ba t)()(21tt,2ta,1bt,12tt1121 , , a btt,11ba,iiba0圖4.12)(t)(t,ba)()(222tabat，1211( )tabtt，|21tt221*ttt2122121bt tt，11212222()( )at tttabat， *,t 開始 確定a,b ( 51) / 2 2()tba 22( ) 12tabt 11( )t 2212bttt *12()/ 2ttt*( )t 結

7、束 N Y N Y 12tt 11212,attt222(),( )tbat 12 圖4.13 )(min21tttt)(t,21tt,21tt0t)()()()(0201tttt，)(,(),(,(),(,(220011tttttt2210)(tataatP圖4.14 )(t)(tP，)()()()()()(222221020202010012121101ttataatPttataatPttataatP0a22110210102210220202()()( )( )()()( )( )a tta tttta tta tttt，)()()()()()()()(12200122021021221

8、22201ttttttttttttttta)()()()()()()()(1220012010121202ttttttttttttttta2210)(tataatP0)(dttdP0221taa212aat)(tP)()()()()()()()()()()()(21220101212022021021221222021ttttttttttttttttttaat,21tt)(tPt)(tt0t0|0ttt)(t,21tt)(tt,21tt0t0tt 0t0tt )(t)(0t)()(0tt)()(0tt)()(0tt圖4.15 圖4.16)()(0tt0tt,20tt,01tt)()(0202t

9、ttt ，00( )( )tttt，1t)()(0ttt0t,1tt,2tt11( )( )tttt，0t2t)()(0tt0tt,01tt,20tt10100( )( )tttttt，0( )( )tt2t)()(0ttt0t,2tt,1tt22( )( )tttt，0t1t,1tt,20tt,0tttt 11( )( )tt02tt 20( )( )tt2210ttt2)(210ttt,01tt,2tt,0tt01tt 10( )( )tttt 22( )( )tt2210ttt 2)(210ttt 開始 確定 t0,t1,t2,要求1020( )( ),( )( )tttt 按(4.10)計算t 1tt