26
0 0 4 1,444, 1 (AA rxqo IAA/ 6. 4 1 . 44 y ( 7 , 4 }- 1 ?, I 7777-1-ftr; Of 4- ) , 10 7 6. 11_ 61 -4 ' • "P-44J - (--7 . ( X 7 ) 1- -71 1-7. 9 ci k. 5. • i .. .•••' 1 -1 •A1 fw .1 ,- v),„ , / • ( 5 .71:Lvv- .3-- aA.d .1 0 *(1-7 '751•A'441 11A4 CIO A • 1-4/69 )6(kF tAvvet.A.4. (AA 4 1-5-ar l,W1,Vt t I L'In 4 1-Y (1 4 4 t -, /leieviir•O LA-01/rki ro-u•4:-1,11.147 1 11 f/ r - eyvv LA' , •‘ LA-5,7-11-7-0-4 .cci a C 5 1 ; "14: c7/vv )73 0A0),5 td.v2e, •••-rier? . •731 - 14-71 , givol dv LA- 4 -4-4 V (7/ . . 1,6-71/11cA i . -1A411 d arit VA-1

CH#1 Introduction

Embed Size (px)

DESCRIPTION

Optimization Lecture By DR. Tahir Uet Lahore

Citation preview

Page 1: CH#1 Introduction

004

1,444,1 (AA rxqo IAA/

6. 41.44y

(7,4 }-1

?, I 7777-1-ftr;

Of 4- ),10

76.

11_61-4'

• "P-44J-

(--7. (X7)

1--71•1-7.9ci

k.5. • i...•••'1-1 •A1fw.1,-v),„,/ • ( 5 • .71:Lvv-.3-- aA.d .10

*(1-7 '751•A'441 11A4 •

CIO A •

1-4/69 )6(kF tAvvet.A.4. (AA

41-5-arl,W1,Vt t I L'In 41-Y

(144

t -,/leieviir•O LA-01/rki ro-u•4:-1,11.147 111f/ r -eyvv

LA',•‘

LA-5,7-11-7-0-4 .cci a

C5 1; "14: c7/vv

)73 0A0),5

td.v2e,

•••-rier? . •731-14-71,

givol dv LA-4 -4-4 V

(7/ . .

1,6-71/11cA i.-1A411 d

arit VA-1

Page 2: CH#1 Introduction

`.•<

;-Lexiy;

Y-Efri tr-in

f2&t:(340-b-W1 51.01AL, pyl,zni- _

op t 76 PLLWY) 11.140.G1, &Lc1 "1-01-1-71

414 e-s11-Y1

V e-e-to-e

7t":1 Vt. VaNied14

1.111 01 vv..);

)

smk3e-i-t- tt, 1-, ) Cenn s-71 ak%4L

1?- ;

A-r, 671 s 5 1. 1A;t5

f(X) 411 4n6 t aMetiek tY11-4,vv; ; 34,1-4:071

t441 rt eL tyL,v, a. 4e-

Page 3: CH#1 Introduction

) n1

L-7

,

ot) 83J4 11-4,Y? C-1441'005 d-e-i-) klin.,,e,T

0 i; LL; 2/541--txesvo)

e44,

L

1, ) 8 ov-,e...04 01,-) totl/vvi i ss-; taitAt es. t

■(' avyY)%ri

PeS7-, Vedkitt..

ea,

■14/Y

fA:ixeek

) ef, coo YL-ts-r-)- sefm., yout,„ez, owe) wv1/Ple.1

be,3 e c ULAA,L

tio

3

Page 4: CH#1 Introduction

4 5 7C-Lif -I— -± 5

A stovl-Rt. vbvyia-tot2... cp

f-(71) f >J..) 11)

►'?? ; V/ ; rY) Pi/V,V1

- fen- e_

0-0 <

(x'') ( -4- In) LI ) \■'v-)<,. I 1-1-)

0,- at-Gs &tufa._ )

ft-A) ftx ) tit/145,X ; 1.4.4.11

Art.) t, -f-i W11 Yl 1 NM 1-A,1"elerr riA.611-,X. f 1,11 1.4-1,1")

la 4.4-k- e)crr 4

Or"

(x)

c'`"

) (Y.0

'4" ) ) f °

f ) 0

f 7 0

S 14 Le tsv) eavr

; j ry.M."...1.--) tlY

vrtik-9( i re) wry)

5-- Of- 6e? ext! 3

Page 5: CH#1 Introduction

-2114 `g-

H ) )

D(4)105

D(!,1, <

(e'r 1°)

c■ -) 6 5

VJ -.()D C-AR t."1,1; Vii VV,Ot

(a J c fijj t—d 0,1

4 4 •_.0pIL4vIp.a.; CA t9 tz, v 4.4c ietitc, •

H-e-c5 A-1.1 khAt ),,c,

H -ct,t1)

(.,t1 -as

N EnA) (ez ,40 II Gi (-VI 1311-41A- z96 e )

v -̀a (A,6)

3 ) (6. ) < J 114„t., 10) A set,!eLL p rkAi g cf

L A, Tkt., 6) CPLAA

r tn,1 t thAt)Arei,

-r-vvv\ tetA t C_ 1 tu-Le) A.-10-&-0

1{ e. j, 1pdSi ASS.. ,e,4 Its')

C.,y• 69\1 p t-v\t, t ,Q,Dcakk vd♦ vl,N A

4:k

3) ..‘„ ye, #' C-14e?-11", r pat

1-/ R. 114 Sort.

Page 6: CH#1 Introduction

vIcett5

P -e4

co 5-t tx . t

-

tn6

i k & •

Cj e4, 12,41.1.4A vorta- 141

:fr.- Y7 octal V:

r ;LA

- L It 1- 1

a

E ,fLL3 c vaAvfi_ 117 4•-• yalm rv•-■

c-4/1 5-1.1 FA.114 5 1,1,- A 60-1,v1 YY-0-4-vA C kat W Zry

0

estja r 044,s, TkkertAsytt.

s-o-vvyte. A

‘114,14: YVA-4•014-"' r

( s-) (1-6) 7C. ) 1. 1" 4 4

(v. k )

I [ I, r

i2") " 1 9- .S"

.--- ..,

i 0 0 (w,k)

_ a •4 3 ' " 1, < t 5

k..., v, ., V E

Firs' (1 5 ) Us) 051 :If)

— -X- 0 41.1SC) 7C

ed - "4 sm -:-... 0

I »AIL t-i

? i-aa si Pots_ (.15) , ('5) -/- ■ 15 — 0

c6cme,y,

5 (ck)

til

(ry, k)

E 7x- ri. • (2.0e)

b. 6

M50

V

CçL 1 i ecrli 5

L

Page 7: CH#1 Introduction

4 L

Z.

L C

t A

5

rei k 13

-: -.):4 :tril \A \

J

t

tj`A

• '---,

1-7\A • IA -A55"ip) r?a4vvvv)q.

Page 8: CH#1 Introduction

AX

X .7, -0

C t x

x 6 R mxn

,DE R. x

b s t

s 10

Sti -/ o

7L

3

t e. .

)1,) ; 7i.„ C. -1C + Li 7( — X 7

— s .t

e.,c k1-5Y-'"

VV1 x

A X. to

3 .4 C.-ery)51)rth..‘4•0-

&I)

cj,,kmr),)

L

AA. 4.

L-irm7-

Two -ft5Y)" 5

OVY shk-J<-

tie"' x ‘.•7 c*-re_e_ wart

s • t. "X- I -I-

.7C- 7C- 2- 2- 2- 7/ 0

3 -k - x z t , 7L-L. 78- LI 71/ C' = o

Page 9: CH#1 Introduction

L-111eck-le Pve"A-rett-^,--ln vs-) i/22

YV11 Y1 9 ylel 1 lye -i-

C714o-e2Se a v) \--1"-v7 .2_1 -7. VI:-

vy) 11

f,. tr_ CZ.

E I

- 1Y)

12 lila", t 2,0 eAL322'1

vArri APL.,))

s

c -4

Se> )1,\AL

S w\ 1 NeY1 1 e, e •

t

A x

Page 10: CH#1 Introduction

°

Y) et,y. FY 0 Trot-yr) ■-)-1 kyl‘.7 C2)

. — p Crt-vi 15

X

c9 x 6 )

ftTY Fc7,64.612 2_

X 2_

C

•Ic c R,1 r-s ck-t

X C

6

E )(owe) s .i; to ct

ely,.4-1/030 5 C A x

cw) at (Si A e.

C-rl V C/N( St- 04).. tr•WL

E. V ett CO.vv‘ toe: -exto r e45 Q.

›.)

Sattk 14-17,-y1 SGL et a tg vv.

Page 11: CH#1 Introduction

A.& ct-14-4,11

Co-6 6.4 elvt, Ck

/1 Cevw SeL,

fey .P.,.ett,tel,"g A S S 17 v' vex i

io r J

x 2—

(ko

kt YIP—)

6 ' '

1,9 C criN ex.

O .5 6

6 - )

4-4,A-f-Ar r•vt vvt, e7 c ats biA.c.,

. , tA pvl.ftet

ett

>(' I C4- z. -*

et,v1-1- .v) A4144,11 )

pol,v)t5 7

e

A n 21„ 0 • -.4 C,

Er<

te.

V 0 i R

Page 12: CH#1 Introduction

eta Carry cx. 6 uk., czy,

v\c)-1._

tsr-r 1'1 ;■".. et

51.A-14) s, ce. et. CA:5v, v e & e cfrno

ivicrre- Ex 41,,,, 7 if

C6vs V f4t,

e-vu2ey 94.11)71141').

Lei (..cry) vex

6i. S D. ;7/ C' V

-- •

A

to-eiv.eieS (ç4,64-4,d) ccv)vot

r

yL ev ve.‘e,

Page 13: CH#1 Introduction

r _ etC-

A 5it Ct >4 e_

A t,x a-2.Y

C

a X - Caterfz.A. et r

A k .9b • e?-17,6.. YUJI

rye, ‘,/ •C-K t7rvv7.'14) i A.1,4erro

e-- 5 t-L

ciuLA 5;1,4 et ke-eptot

lt, v ke..- 5 Pa. ce, t4i.1.12 Spet cep

A 1,11944._ p .PCOVVI 1k9 et.44,Ltr) oipt.„0„,,t4t7.1 1„).

th,to

Fry Ot eve g

0 V a

vex

65-y, v.f-x titt

k cc

likt4,v,ry)

• k

k

Page 14: CH#1 Introduction

C e ve x

Atscir ; 694 ai-o

/k A R

n v hU "16 T-

(9) ve-v A-J

Le-y)

eat ye-r)

A perel Y-trn

S CL >C. " A

otp x) ( y 7, A 61 —

4- —).)Y

ct_c r\s ( —A)y x

h 6 Spa c i-s < v

— vex1iIALL

k/.04. lAtt.tt 11.

tr veK

to IA.44)s ( P

seatry) (a)

6,6 Lery)V Ems. C-ern veu

be_ 6,0-invey

i yt_aLfz.)4 roc

1-E 1-

y 6 S v, V 2-

•,‘ svv, cz Sv s

a x

K 5t...1.-p-pz.,Se, x OVre,

grP19f . A 1 e R 11

.

pe71-0.1s L1A- ciA-G-1.1 1 /1,,A at_

1 ,,„.. tv 1

??' A s y ,, LI1 1 .

hc096 ,ice.. • 1) ), r , 3 ,

Page 15: CH#1 Introduction

S

S.

;./ >rw 51.4.. LC 14-td [,9

A Y

r rY) Oe

A cr vX (.,,-no-vv1,,

jf, 10..e.P try)

/5

Cfcrr.

V V t

A. 5 X;, E. S

S X I F.. 4.1 st I) 'lie_

ar X 7,, JI >,

I., w.

1,1 1 I - - wy

„. .,, 17 nti,krbok i- 0," 1,) 51./Le., t ,̂ AAN st 6-"L"'"n

■ LAI_ 'tf rzykt

„A)

(„6 n & eAlurrvi)

aiesAA-mi e, try-0/

Sa e LrYtS. -L, coz-t,

(t w„")7 5t.

fr

t--Arvert-c-

turt.i.4401.21.>

r

■ "V”

Y

fn. y■ te- v)t) . eo 4Avv-a,,,),,t,<).

x. k ,

Page 16: CH#1 Introduction

se tertl

r

Crr ILA F iket-e- e•

N ct

.... ( 1'1'

P e FY -LI Iv err) . C-15"A4'i Ott-t, P

tac

s,(A.c.(-1 )1A bt.t

. A v pt,4 r QC Ct

- (A- c.),AA.A4-.

--- - - ....... ....... _ r.

C6Y1-5,-; ekk, A r e*-9,P-A kulirr-in P . R I (._

et -7- x.. ,. to -..,, i.. c 1-- ■ t 1.

ek e

T

vect try

X r ..r. 1•11 2_01 3 — 1

CC'V.V (.)

X

cAt'vc--vvr) ra--w‘ e Co

Page 17: CH#1 Introduction

S it,t1.45H1

p b c. A. Le

VIA, 10 7. Wveglitich lotj

"114,1,v,

cry) S tr.10;11

VA,Ciete4werer)--1 Ay■

•,)

/7

t,\4, •

AL x.

tAr c'? • ,3 t -?( 1,4. e „ x /

i co-t C kelj

g.14,4A ,•)

(A) d.t.e,„ PWC. e Ve t. Ivry- e 1 e

't‘"Aett61°'‘,Y.It

() R 5 F

("P ) f4

t .

44

Vte-tirrY1,5 6 I;

A- 4 ttc et),44,

Plr crPfs Pe re, 4, 1.2 .f—rs-r A'Yei

LI-t) L>787"

ovic- Pill r4,1

) - -c 'AI4'13 C irn 5 tr d41 r^S

n)

Page 18: CH#1 Introduction

Nen")

k se-L4 11-0.1--) •

, et•-• ') e-ov..) 6 Ae_ e,\AA4-toi .S

.41 ) rcrt 1,44; c_

E

> 1?) , c ,

ciak Av

A,-y

PV1 C

sio-thAt'vrre) , )

eter-C.- ty 4.,--o

f

7

A , 5 , , owye, AAA"

i

A

v, ivet4,1c-

vs.-)

c. evw) Ls

Page 19: CH#1 Introduction

ki p -)

( 4-) v)tr)+1 •

@I)

(A)

(k,)

Fp

A•4oe C- f $14,..1

.tt eme F. X "i"

rerllea-

Lt_t e 4,-„t A Ve,r1fX di+ r.).-**)

P 75- Y -1 c

NEY-tA.) ece)5.e-

y

p C,

X

—. ./Y

Page 20: CH#1 Introduction

& P ftp‘-‘,;i0A. •

401, We._ C.A-1/1 ;(- 17-) t9"1-. 61,0 -e-Xtr&m.f2-, zywa-

Lej,

_ L 10 A2-6 Y 140;

1)-yrp s,T21 te,

X -I- E. A —

t o X

E-: t3 otivi c_ s,,,LA71,„ -cry)

ye_ Lel tA.,%)s s

v) r,191 _F-e

oG z Se, tisat,

g- 2;- ) )/7., ,)` -f-- •-c

SD )“)L

PY c'ef C R s p

AAri E>otta. of 0.6 r cti. 1,, to!

olAw. stbia ti,v)

D tre-vid.4 )

taffue.6-Gv7-t_471-1-c-r?.

Page 21: CH#1 Introduction

(MAUL. Are (2-

C. .4 14- • —

r

R. Y1 tel) 4,-. 1 Y Ar+eln.A-5 Fja/,,1 C {A? g"....c-; to le

1\1 -L.:, •

P 7 X e

1-1

1 /14,•p• v)t..)

• 47-6 1,1,1 Clerr)

601.4-i C. f eesk,Se; .

5- /wiAAlt-6 (-we

h

CN !mum

Ev ,1)-4-1-14-0-1,1'

( le„) t,*(4A..,

"=.

)

et/re... C24/11

O

J110 r

1:4-o A.e'r

Covi4 t•es,1,4)41

e

f e Lac

ek/tol A Sea-ti

CoCCet4

nlfb L:51-7.S.T.reavv., 16, A x x

\ A . p.n.)

A v e Crte,"--1✓ Ok.e"; c.

" r

j = -

I -CI 4 ir e4i

Page 22: CH#1 Introduction

NW,

e-6-Y? "I- 4.)

44„;

A,N-A„ eke e=6)Tel-411-1 s

A 131 , )

A &

1-t.” • e, 1 1 .11.1

S Lel, 3 ; 6 b

.81

, so-,-,vc

ft '1/4

.) 10 44,7. $--6444/1.4v) ',,C,

vet/y1

A c A g ) - - , eVY 45) 631."5-1 * S J-1/K-C.,Vvr- )

eC rn 1 kt_

10 01546 g7

22

A A 5

\L)

Page 23: CH#1 Introduction

<1." N.f.) !.4 -

CID

L>Ak14) A

( A ) k. < -L

77' /Aus-tA, ef — -

Lev, CLL. • .11, •

-

r

f/er.el GC- .4-1,1")

YA,vtg- (4)k 3

t9t

)crtA) k

27-

23

Lei

k 2L A i

7 I

sp7EP

Page 24: CH#1 Introduction

:)? e-yel c46i . ; D e-

-7)e--6/e)■ A- 044 s x c le9 '441-24.1.1.- Otte,. P . -1

Cil.1.44-r_. rr

vv) 42_

Li'-"er-Y7 5-r-r

t

.`; e re' 1 A 6 01 S o-61,■22.0-7

x

A BY ci

Vt cri-7 ott,I.L,Y),e-Yotka

io C - 4,177'

t`>i )

et4,1 c-e@' A-c-xece-yfitit-t-;

C. 4441'e,

x f--e,v,tf)

4 - J7p (Arn tovvvi.5

x A 6

Page 25: CH#1 Introduction

11-AL-13 enfr)

171A-1-1, frEtu 5.7

S-e-AA:t ) P

, ewe_ gi 7 ),2 ) --- )"11

ppliSA.L.4ky Cvu2-nr 1-1.221,- try-) 1,3-0 4-7--L.4141,4

In" key) pCt. j_10.6-1 ‘77-7-e_ 4'51.6 fe.A.Ari 1911 S 0-CA(4../5";') .

, Prrwyks ort,t vv? t

6 Cfv, er;

ilnk 01" t/vein tAii v) vv")

J.

P. i).17-14,-vt

pL

F el ex, (.45-kin avv,

Pa,' err, e-tellel •

c.„_t cry it 1- tr)., ettlAA:LS

Ct, y- .04VY

VLI41 V1,-4—r) ty-4,.-4..e.,e4

(.1' P >e 6 , 0101 C.w1p-r(/

es2eit4,-; V A/ye,

P tA-6Y)LLL

kw- • AA

6"re't-Wv;\it-

ett,Ct ytetel"-er, fr

rt.4,16,1, (kg

iiLy °AA C..1" Ovvt

Page 26: CH#1 Introduction

7-141.-nr•-

Q CF

1/10 kik"...Ad) Cf-

LJ

›c' C. :Q

ese NovA)--- els Q. e_ wP

442 s)1,, X lo) ,>\,„„ tAt+rt- f t

vN, (../ CtrIri It-Y- tMetevr.-- CY "1"AILI t'6 • p

2

S IAA- CR—,

eN)

,

-r r) C X C

c„ 1

Plrf2. C-1)Ca t

• • t

A

'1)

VIC; L 6w, 't

r •

Q • it/LA") Ott attr),) re) 1-1-4-1--1

PI rot: Lel 1.0 e,

so-OA/L1nn

g ) A x 2 Id

L e- err- trtnel AS V ot,,e-R.L. t to SA-,