1612726871-fb2580394fa55ced84747c959fd39192 (Глебов, Кочетов - Учебное пособие), страница 6
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C!),f^ = f (x) = f = min f (x):x2Q) f (xk ) > f (xk+1 ), 8( )( x!) fxk g !f (x) = f (x ):D! ! !!.4.4 3 .6 .4% ! -+ !!( :8 ! * /!. I + .!,+ ,"(. I! ! !8! +( !!81f (x) ! minx2QQ = fx 2 Rn j 'i(x) 0 i = 1 ::: mg(4.26)(4.27) !) !! !"Fk (x) ! xmin k = 1 2 : : :2Rn(4.28)* Fk (x) | ! *!)! ,", ! ! !, ! k ! ! !!) +( ," f (x) ! - Q !!! !- Rn n Q.
Q( ," Fk (x) Q , ).+ k - *!) /( ," ! Rn *!) !+, + - Q, .!! (4.28) -!) + + .8 +( !! (4.26)-(4.27). / ! ).( ,"( Fk (x). H !) ! ( ( ," Fk (x) ) ( !".&" 4.2 : Pk (x) % - 0 ( k = 1 2 : : :0 x 2 Q+1 x 2= Q: Q, Pk (x)x 2 Rn (lim P (x) =k!1 k /* , ).+ !+ k !!. x 2 Q + ).( .!,, ! x 2 Q / .!, 8 k (. 10).820. 10. V!, ,"G 8* -! Q - ! !) ) * * .!,+ ,"(. ) ?a]+ = max(0 a) g(x) =mXi=1?'i (x)]+:D) - + .( ! Q = fx 2 Rn j g (x) 0g .!, ," 8, !, 8::kg(x) kg (x)2 ekg(x)=k (1 + g (x))k ; 1:) .!,! ," Pk (x) - !!. -Fk (x) = f (x) + Pk (x) k = 1 2 : : : !), inf F (x) >x2Rn k;1 + k = 1 2 : : :(4.29)D*! !-* k - !!) !( . !! (4.28) ) !)) !)+ .(.83 -!8, - *!) (4.29) - *!) + k.
/ !! !))8 (k) !(, (k) > 0 k = 1 2 : : : (k) ! 0 k ! 1 :)8 !* ! ( !" !( xk k = 1 2 : : :, 8: 8Fk = xinfF (x) Fk (xk ) Fk + (k):2Rn k(4.30)G* !, * . x !) - . xk *.)8, +:( (k).I, , : *, xk - !-!) Q.G!)(. - - ! *, ! !(! ! xk . / *! - :! !* ! ( !8 + ! .!,+ ,"(.) .!, ," Pk (x) !!8 :)8 *!)+ ,"( Wk (g ) !! Pk (x) = Wk (g (x)) ," Wk (g ) !, a) Wk (g ) + k = 1 2 : : : Bb) Wk (g ) -), !!8 g lim W (g ) = +1 g > 0Bk!1 kc) Wk (g ) + 0 ! k ! 1 ! g 0:D*! 8:! ! ! ! +! .!,+ ,"(.
4.6 . f g inf x2Rn f (x) > ;1, % a) b) c) fxk g % (4.30). 51) klimf (xk ) f = xinff (x) klimg (xk ) 0B!12Q!12) x Limfxkg ( fxk g, x 2 Q f (x) = f B3) Q0 = fx 2 Rn j g(x) 0g Rn 84 0 > 0 , klimf (xk ) = f !1(xk Q) = xinfkxk ; xk ! 0 k ! 1:2Q. 1) 8 f : !)) fy m g y m 2 Q ( f (y m ) ! f m !D*! 8* > 0 !( ! m0 k0 !, m m0 k!), 1:f (ym ) f + (k) < k0: #! g (ym) 0 c), -Pk (ym) = Wk (g (y m)) m m0 k k0: /+ ! ( f (xk ) Fk (xk ) Fk + (k) Fk (ym) + = f (ym) + Pk (ym) + f + 3:f (xk ) f :C!), klim!1L!, k k0 ! !Wk (g (xk )) = Fk (xk ) ; f (xk ) f + 3 ; xinff (x) < 1:2Rng (xk ) 0: !-, 8! ! klim!1-, ! !.
D*! : !)) fxks g, ( g (xks ) > 0 +s, ).+ * s0 : b) 0 < Wks () Wks (g (xks )) ! +1 s ! 1: .2) ) x 2 Limfxk g: D*! : !))fxks g +:! k x: 2" g(x) !, ! ! !ks ) = g (x) 0: Cg(x)0./limg(x !, klims!1!1!), x 2 Q: ( f f (x ) =85ks )f (xslim!1! +* ! !! slimf (xks ) klimf (xk ) f : / f (x ) = f :!1!13) G!-, !* !! klimg(xk ) 0!1 (xk Q) ! 0 k ! 1: -, : r > 0 !, 8* s > 0 !( ks s, * (xks Q) > r: 0! !)) fxks g: klimg (xk) 0 , : N0 !!1(, 8* ks N0 ! g (xks ) 0 : D! !- Q0 !, *! : - !), !)) fxks g + x0 2 Q0 : ," g (x) g (x0) 0 ,!), x0 2 Q: #! !) -! Q :)8 !! *)! * ! !), 8+ x0 x00 ! !j(x0 Q) ; (x00 Q)j kx0 ; x00k:C!), ," (x Q) | !. D*!(xks Q) ! (x0 Q) s ! 1:/ ! ! (x0 Q) r > 0: - .
! !, x0 2 Q: . ! !, !! klimg (xk) 0 (xk Q) ! 0!1 k ! 1: !* ! - ! !), !g (xk) 0 klimf (xk ) = f : D! ! !!.! klim!1!1 !8 !, .!,+ ,"( -( 1!*!-!. ! , ! ," 1!*!-! *! !! ! "8 ,"8 -, - !!!) ! .!, ! !. 8:+ *!(. G ! -( 1!*!-! , 8 *! !:86/,," ! .!,+ /,,". - -( 1!*!-! !*! :! ( , ! .!,+ ,"( - ) !) .+ ! !! !).87 5. !% G + ! !!!) !!, + ! -! + .( )+ ( !, !+ ) ,! !) !!), ! . ! !" !!. I! ! + -+ !8 !!, + !) + ( ) ! !) ! ** (! *) -!.
H + ! ! "!)+ . + !!. / ! ! !! (@-.), !8: +(+) !! 1 ! ! "+. I! -+ :+ , !!31 !!:cx ! max(5.1)Ax = b(5.2)x0(5.3)xj | ", j = 1 : : : n:(5.4) -.- !! (5.1){(5.4) !) !! 1 (5.1){(5.3), !8 +( !! 31 !! ( " +.I8 8 * * (.. "*) !)* . 1-!!" . !! 31 ) !) +:( + !"(. - *, ! *! , ! * * "* .. *, *) , + "( ) * ! * ! !8 Rn , ! !8 "( ,".88! ! !! 1, . !! 31 8 !*, ! :! !!! 31 ! ! : !* !) /,,. !: ! +(! . !! 31: ( *!" .
! ) ! , ) !8 ( !)(. ! - + ! (* *!!.5.1 &$8 6 -, . 1-!!"8 !( !! 31, !, :)8 !*- !!! ! !. !) ! . x0. P . 8 ", !) . !!!( !! 31.P - x0 ", ,! !!! 1 ! * *!. G! *! (! ! ) ! !, x0 / *!8 (!), ! . !! 31 !8 . ( !! 1. L! .! ! !!! 1 . ! ! .!* 8 + , ! . !! 31, !- ! .). : ! ) !* "! *!!. !* !!!* !, ) * ! :+ -+ !!, ( ) !*. C!! ! !- G!"*.895.2 "$ " C( ! ) ) .!8: ! ! ! (. + )+ *!(, !) !*!+ ! !*!+ .
! bhc !! "! !) ! h, .. !). ", +: h.) (! ," = d0 ;Xjdj xj(5.5)! " "!) ! ! - + .( !! (5.1){(5.4) h 6= 0. P h | ", "!) . D*! 8* x, 8:* . !! (5.1){(5.4), 8 8: .:h + Pj hdj xj = hd0X!", jbhc + Xbhdj cxj hd jXbhc + bhdj cxj bhd cj0(5.6)0(5.7)(bhdj c ; bhcdj )xj bhd0 c ; bhcd0 :u = (bhd0c ; bhcd0 ) ;Xju 0(bhdj c ; bhcdj )xj u | ".90(5:50)(5.8)(5.9)(5.10)(5.11) .! !. + (5:50) (5:6) ) "!)) xj . / ! bhc = h ! !, ! ! !*! (5:50) (5:6) !!8. ! (5.8) (5.7) 8 ) ! (5.5).
!(5.10) /! (5.8). (5.11) ! !), u ! ( ! ) + "+ , ! ,( !( ! !! (5.7).D! ! , ! ( (5.9){(5.11) *! !! (5.1){(5.4) -! !! 31 * - ! /!8 +(. ( !! 31, 8 ), -) - !( - )+*!(. ! !+ *!( - ) ! !, - ) !! 31, 1-!!" ( ! " !) ! . ( , +!!!! 31 ! .!).0. !8:+ + !* "! 1-!!"("! ) ( -. H ! , ! !!! 1 ! ! * *! * ! !( !) . :( !!. /( !" ! !+- !( !+- !!)*( * ! ! ( !!. / ")8 "! . !-( 1!!"( , " ", !( !! 31 ! ) !) *!, !! (* -!.5.3 +. "-(LD-)I! ! ! -!", ,! ( ! ! !) ) !.( !91(. ! 2).) !!!* ! ! B - ! + + ) S 0 = f (1) : : : (l)g, l = n ; mB - ! + + | S = f1 : : : ng n S 0 .
! "( ," ( !!( x0 ) !+ + ! ( :, ) (2:100) (2:200) ! ! 2) !!) 8:! :xi = zi0 +Xlj =1zij (;x (j)) i 2 S f0g:(5.12) / ! ! !- - .! xi = xi ! + +xi = (;1)(;xi) i 2 S 0:(5.13)C-!"! !) ( !" /,," zij !+ !( !( (5.12){(5.13). /( !" ! n + 1 ( !-( (, 8! "8 ,"8 x0 .
E" ! l + 1, + 0-( - !(, ! !) !+ ! ! ! , ! j - " ! x (j ) ( ! ). !, ! (j ) = m + j j = 1 : : : l -!"! x0z001;xmxizi0zi1..xm+1.xn..0.0+1z01..;1.092: : : ;xn: : : z0l::: .: : : zil::: .::: 0::: .: : : ;1 j ! j -( " -!", ..j = (z0j z1j : : : znj )T j = 0 1 : : : l:D*! ! !( (5.12),(5.13) - ) !! !(x0 x1 : : : xn )T = 0 +Xlj =1j (;x (j )):(5.14)P zrs 6= 0 r 2 S s 1 - ) /! ! ! ! !, ! ! !xr ! ! ! x (s) 8 . /!! !) ! (5.14) -! ) ! !! !-! ( ! ! + +.
G /*! 8 x (s) r-* ! Xx = 1 (z + z (;x ) ; x ) (s)zrsr0j 6=srj (j )r 8 !( ! (5.14). ! + !(x0 x1 : : : xn )T = (0 ; zzro s )+rs1 )(;x ):(j ; zzrj s )(;x (j )) + ( ;z s rXj 6=srsrsD! ! , /! ! ! ! !, !! ! ( ( x (s) ! xr , .. (s) := r, (, - !, !! ! ( ( xr! x (s)) ! ! -!", !+(:8>< j ; j ; zzrsrj s j 6= s(5.15)>: ; ( ;1 ) :szrs93sC-!" ! !) , !-( " j j = 1 : : : l *!, ). .5.4 &" LD-0) !!) !)( -!".1) P -!"! !,..
zi0 0 i = 1 : : : n, I P3 (!) .).2) !) :8 r : zr0 < 0 r 1.3) P fj j zrj < 0 j 1g 6= , !) :(" s:1 = lexminf 1 j z < 0 j 1gjzrsjsjzrj jjrj! I P3 ( !!! ! .!).4) ! !) -!", -) (s) := r ( ! .!* 1..1) ! ! (5.15) +! !)) -!", - ) ! !, :, - , ! *!,*!!! * -!.2) ( " -!" !- !! *!, ).!:0 ; zzr0 s 0rs! ! zr0 < 0 zrs < 0 s 0. H ( -) ! , ! ) ! !"(.3) G! :( !)( !" ! .!* 0 8:. ) ( 94 -!" " s = lexminfj jj 1g *!, "! P + +.( !! !j 2S 0 xj M .
D*!P! *! xn+1 = M + j 2S 0 (;xj ) 0 -! + .(. G () !" ( (n + 1)-( ( (M 1 : : : 1), 8:(( xn+1 , ! ! : " s :( ( r = n + 1, !)8-!". /* !8 - !).5.5 &" "+ + 90) !!) !)( -!"( !! (5.1){(5.3)). -) := 0:1) P -!"! ! / zi0 i = 1 : : : n ", I P3( !) . !! (5.1){(5.4)).2) P -!"! !, !) !) p 1 !, zp0 | ", -) := + 1.C p !) '.H( !xp = zp0 ;Xlj =1zpj x (j ) ) *!*! ! . h = 1() *! xp ):xn+ = ;fp0 ;Xl(;fpj )x (j ) 0j =1* fpj | ! !) ! zpj(zpj = bzpj c + fpj 0 fpj < 1).95 -!" ! (n + 1)- !,8:! ) *!8(! ( ( xn+ ).3) !) :8 r : zr0 < 0 r 1:4) P fj j zpj < 0 j 1g 6= !) :(" s :1 = lexminf 1 jz j sjz j jrsrjjzrj < 0 j 1g! I P3 (:! !!! 1,! !), +! !!! 31,! .! *!().5) ! !) -!"B-) (s) := n + ) (n + 1)-8 , !! !), ! (s) := rB( ! .!* 1..1) Q! .