@KN R))< - 東京大学tanigawa/classes/H30/lec10.pdf · o '¥. is. LP EFFF < lY'¥4 tin. 3 (D) Max...

9
FEIKHTEI a 't '¥s7¥ !1! AER " m , BERM , CER " ( Ip ) min ctx sit Axeb XE 2/10 CIP ) a LP 4¥a4r : * ) Min CTX Ob : ( IP ) = ( LP ) se AXEB Lp a¥aiE' Fear . 'EEkn" " tn X=° ttb Ipa t¥nfdFP LP a 77kt - ' (D) Max bty FFH 'H¥E¥ : ( LP ) 2 ( D ) s . t . ATYZC yzo Dttx , 4 :# KIFFE , otx - bty 2 ctx - YATY = xt ( c Aty ) z 0 4

Transcript of @KN R))< - 東京大学tanigawa/classes/H30/lec10.pdf · o '¥. is. LP EFFF < lY'¥4 tin. 3 (D) Max...

Page 1: @KN R))< - 東京大学tanigawa/classes/H30/lec10.pdf · o '¥. is. LP EFFF < lY'¥4 tin. 3 (D) Max Z Juv UVEE situ Z Yur E WW) + vet UV Eflv ) Juv 20 tuv EE A V it Battles

FEIKHTEI a 't '¥s7¥ �1�

AER" m

,BERM

,CER

"

(Ip )min ctx

sit . Axeb

XE 2/10

CIP ) a LP 4¥a4r :*) Min CTX Ob : ( IP ) = ( LP )se

. AXEB Lp a¥aiE' Fear .'EEkn" " tn

X=° ttb.

Ipa t¥nfdFP.

LP a 77kt.

-

'

'

(D) Max bty FFH'H¥E¥ : (LP) 2 ( D ).

s . t . ATYZCyzo . Dttx, 4 :# KIFFE

,

otx - bty 2 ctx - YATY= xt( c - Aty )

z 04

Page 2: @KN R))< - 東京大学tanigawa/classes/H30/lec10.pdf · o '¥. is. LP EFFF < lY'¥4 tin. 3 (D) Max Z Juv UVEE situ Z Yur E WW) + vet UV Eflv ) Juv 20 tuv EE A V it Battles

III ( En KEEFE ) @

•¥h An '

'm Gilt .E )

@Set a

"

one⇐5 t eeE

,Jens to

•w : J → 112=0. •

Is wlv ) ftp.t a Air E Fixsh ' '

.

( IP ) min [ Wlr ) Xv

vet

st. Xu + Xv 2 1 te :{ a. v } EE

Xv E { o.

I } tVET

>

( LP ) min L wlv ) Xv

VET

s . E Xu + Xv 21*

e={ a. v } EE

Xvzo tvet

* L Peek 't Atutu # ht 't But ''

' )7i4

• (LP ) EFFEE.

knt¥xFd' AEEXETSZ .

• S = { vet : Xlv ) 2 's } EID .

ThM_ I 52 3nA"

Y 2 "u IF 2 - Itty

@ • tteeluiv ),

Xlu ) + Xlv ) = I ⇒ a E S or VGS.

⇒ S it Dti'

-

.

. HP ) ZCLP) 2 ¥ ,

WH xrt'

Ityegwtd y.

Page 3: @KN R))< - 東京大学tanigawa/classes/H30/lec10.pdf · o '¥. is. LP EFFF < lY'¥4 tin. 3 (D) Max Z Juv UVEE situ Z Yur E WW) + vet UV Eflv ) Juv 20 tuv EE A V it Battles

o'¥. is

.

LP EFFF < lY' ¥4 tin ..

�3�

(D) Max Z JuvUVEE

situ

Z Yur E WW )+

vet

UV Eflv )

Juv 20 tuv EE.

A V it Battles Es Z Yur = Wlr )-

uvfflv )

¥7717512

. y =o

• As IFK En &"

F- 'Ee '24r to D e= UV at

Fffz Is :

•'

l" 'b5 on Ethier .BIZ 4. FZFZ "

ye qtta.sn} 4 * t

. TEE 4h 7k¥ . #*E E 14 A.

• of in Peru 77ft ¥74.

Th_m: E 77 If ifn a 2- FLTTK.

@ . 4h Ha.

bn' '

-

.

.

y°: ¥a¥E#7t 's Y .X° : 418

.

> 0 1 > s 0• ( IP ) 2 (D) Z LYE =

I }opuY€gµ,

YureeE

> > o

z I L L YurVE X° urE81v )

1- -

=

2 #W " )

11.

Page 4: @KN R))< - 東京大学tanigawa/classes/H30/lec10.pdf · o '¥. is. LP EFFF < lY'¥4 tin. 3 (D) Max Z Juv UVEE situ Z Yur E WW) + vet UV Eflv ) Juv 20 tuv EE A V it Battles

- AE he Far # IF "¥k �4�

a that # Etta M

e I "a7" ¥tFTotj : I "a7 "

JEJ a FREE a ¥ lots

. E c- Jxm : ' ¥44 FFENPIIE.

e th # b" t.tt#fktjZgjhIl

'

a. n' '

E ¥5442 Ee '.

( IP ) min T

sit

,?,gq×ij= tj 1 jeJ )

8 Xij e T ( iem )

jiijee

Xij E { o

,tj } ( ij C-E)

(LP ) xij =o ( ij e E)

A X : E → Rzo ( rttfu, G ( x ) E( T

,Ek ) )

ECDE { e EE : Xe > ° }.

Lent tx : LPEFE 't 974,

Glx ) a # Ittottv.

+ E

qgz :-c " The E¥Ia3 "

' i0 A He Makai

(µe#e°)gu ) atlttieifxti

- E I # Jie # 2"

# Z.

+ E

J M

Page 5: @KN R))< - 東京大学tanigawa/classes/H30/lec10.pdf · o '¥. is. LP EFFF < lY'¥4 tin. 3 (D) Max Z Juv UVEE situ Z Yur E WW) + vet UV Eflv ) Juv 20 tuv EE A V it Battles

7N 7'

'

112 "4 �5�

• xtt : LPEEZFEAF,

GCM.tt#F.EFi*3.

61×4 0

•/ \.

OEMGloblot ° EJMMHIa Glxt ) a 2

" #¥ a I "a 7"

it ¥tBn a'¥4 ¥

.

° #¥ a 't 's " I"

a 7"

it y" In ti Is a F Ii

'¥4 E

Time Pius ' 42 "

4 12 2 - € 4th .

@ e ¥¥ni" an"

j :

'

ERE Pinette tpljsj = Xpyyj

-

. 45¥ it # in ftp. : ± [ tij+ Ipiijj : iaf

¥* ]7

= L Xij + tpuj

j : int

He

E [ Xij + tpcij

j : ijefli )

E T + HP )

E 2 ( IP ). y

Page 6: @KN R))< - 東京大学tanigawa/classes/H30/lec10.pdf · o '¥. is. LP EFFF < lY'¥4 tin. 3 (D) Max Z Juv UVEE situ Z Yur E WW) + vet UV Eflv ) Juv 20 tuv EE A V it Battles

Fa Ek F '¥ 'E �6�

• X i ¥,

"IF AYE Eked

• Nix) c. X i x E X n KL 4¥'s

* Pg FG 4¥' ¥k 7N 7'

'

' IF '

4

#atkAEXe ¥ #

. X e N lx ) At a¥fa E FEE X

'E to #E

• X'

a % $" ¥c IT Ktt

''

X c- X'

. X a th a'

'

¥o IT K it"

X E 4L 1

* His a. HE 'n¥E¥t.

. FAE a fifth e it '¥I at A 12 NK ) ate Fair 'I # Ft

W

Page 7: @KN R))< - 東京大学tanigawa/classes/H30/lec10.pdf · o '¥. is. LP EFFF < lY'¥4 tin. 3 (D) Max Z Juv UVEE situ Z Yur E WW) + vet UV Eflv ) Juv 20 tuv EE A V it Battles

Peak tht 0• Felt a "t7

.G- It , E)

,

w : E → R

o FEE, It t→

±xet

,F' = S ( x )Gfet¥H Ig . ,

wle ) t¥ak a Hat flx ) Efixskn .

( X ET Efixstm . . )

n XET a # 4*3 NH ) E { X $ 's 1¥.¥ ' l Phara #Lan }

.

• IN1×11 = 0 ( n )

That FAFFIF '¥¥e Pna'

'

' 72 "n a 2- # htk.

Q . X : Hub.

trEX,E⇐enH¥¥F"yoff

. to ¢ X-

×¥514.tn?:#t"

Q#"

.

• FI 2 a V 2'

'

4. a E 4 , 2.

• ( QQ)e. (OEO )

.

0,5¥,e.OEO

a > a. ) W ( 8 (X ) ) 12 € Ky Gen a £ LYI

y

Page 8: @KN R))< - 東京大学tanigawa/classes/H30/lec10.pdf · o '¥. is. LP EFFF < lY'¥4 tin. 3 (D) Max Z Juv UVEE situ Z Yur E WW) + vet UV Eflv ) Juv 20 tuv EE A V it Battles

45¥72MEEK 80

. Gilt , E),

L : grin '¥tE,

1L1=k ( Efta )

. to ET,

C ✓ : L → 112>-0 ( vi. . 5in AELESHZNHFH ).

p : E → Rzo ( ' I €A# not " Ft )

• III"

lit → L

• " t " %# 1 e) I

[ Collar )) + I plij )

ref ijeE

lldtllj )

. tell ) Aetna in "4M" be Fin tie '

. NPEEE

o EYFK e'¥ th

. Yat HE 's # k¥3 ( like . a June #a¥ ) .

- : 4¥ #

totact

, l'

is ln a- EFF e⇒

l'

( v ) = lcv ) or a+

vet

Nall ) ± { l .

a-# Hk }

Nll ) I U Na (e)AEL

ten Nall ) A a ¥tz Ec HE it 7g .ir#aIM.zFiFZ.

Cillli ' )a.

sonnetth =D I , th - Db

P . i

ftp.t.se#,tMoFtr@TFHj' ' * ¥.

"

•q

Page 9: @KN R))< - 東京大学tanigawa/classes/H30/lec10.pdf · o '¥. is. LP EFFF < lY'¥4 tin. 3 (D) Max Z Juv UVEE situ Z Yur E WW) + vet UV Eflv ) Juv 20 tuv EE A V it Battles

�9�

§± N ( l ) if a ¥÷¥a Do it.

ftp.ifdf '

off Maze FIFZ.

Thin E IZ # time 44 At utr 1.3 FA t '¥F¥ a 2 I hit.

@ • l : K, H. lopt : t¥a÷E # 4

.

• la : d. 1 v ) = {a ( re loft la ) )

flr ) ( o. w

. )

• la E µ ( l ) ⇒.

E ( .la ) = # I l )

• of

Ella) - Bell )

ltoptla)

t#÷÷tF¥÷at⇒¥F#

in-

* zone.tt?alEe*ainasteftiImljt=:ull#itEE1=ealtZttIe1

'- Eatenz ¢ ll )

y