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PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!wBdrs/shapexml.xmlZn6;Y;^o~($@ˆ1e:VCQ*IyD3t>$}ΐ,{?Cj8ǂQ"N aҏM@.w(ц>㚾=򋣴Snj5y$k. 3X^-f0uӎRnQ$5%ϓ?'N>?4h-'w#N[ O}>Bg!2Zv5ːMktH}@Ϙ2\Qvfy8|t0tqi6Ӥw|Z=;A>i@uOŀqJķRph47=rD !Pgj0:L┙!ZR=S)" c.Y-Aiqrd2HL7 mNEb'cm7_lva$F Ghdv@w<7p>\^6 1n gmyn-(;VP$wÐ!7; % {: ;!#˴LqhGW ]( M!)zYq߳pbR>`!lJ4N`'2EBxqFc-U:smGq] Te;W`FOz=*AT-0#-QrOj~9!*4f"ji."4d`H;[ұ9u:B"29pZt">6> k3rP֖c+ v{U,wql3깎ТWN\㏠M=;W9D.96u+~_?+T Z!!x[5F seV+4\Mb|=.8- |PnoMS;,|,hPvMWUBmFVDx]JW\`hM߂lQ!Bgoւ0cו!km ^Sqeov_^ܠq8'g*qf1ǂ~ҝ.,ʎg\@uSJM;E@Q9X)2U=x6~z2|"9Z[tY[eu.~40]RX}8qUyptMz4.2/v{;St)GL\K㮦UkW!Ԝiu=Q4W3=z <- ħϡNEaΨ'ȇNI\b,\rXV=o0+ 1F$C ɥ58v* Z){KQ|ƙL9d\S\ȘҦ'm@PS KlA+ JAK'kK% SەDpEg<[B"Ϥބl9GAO k\I;Aܞ<>daUaa:vM|`1{i}KMi}5HH(:~a0"YDzp!=NfzJn*J(NECLXiC/jq s.!haea=-2t|Ao}wn\Ğ_Uy 4PK!Udrs/downrev.xmlDN0HHܨCU-7?#$cqhFf۫} .2P,345I Nvˋ Mr rBhcrCղpKj-})mYҖ:I- o:~[}X=̺x[I,j~|yc] /0ws;s#$d,AoPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!wB*drs/shapexml.xmlPK-!U drs/downrev.xmlPK   0^V___PPT980 d^>G5<C NLP? George Dantzig (July, 1948): Harold Hotelling:  But we all know the world is nonlinear! =>385 8=65=5@=K5 7040G8 4>AB0B>G=> E>@>H> >?8AK20NBAO ;8HL =5;8=59=K<8 <>45;O<8. >G5<C Mixed Integer? > <=>38E 7040G0E G0ABL ?5@5<5==KE <>65B ?@8=8<0BL =5A:>;L:> 48A:@5B=KE 7=0G5=89 (! , -:>=><8:0, >38AB8:0, #?@02;5=85& ). @8G8=K: =545;8<>ABL, D8:A8@>20==0O AB>8<>ABL, D8:A8@>20==K5 @07<5@K, =0;8G85 2K1>@0 87 8<5NI8EAO 20@80=B>2. A>1K9 :;0AA  0-1 7040G8 (binary, 0-1 decision making). >45;8@CNB A8BC0F88 15@5</=5 15@5<, 40/=5B, ;>38G5A:85 CA;>28O&    b p T p pp^   Z Y      @` I}OPME `L(  L L  `] ?03>;>2>: 1"XRPK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!b~drs/shapexml.xmlUn@#B!VT8DUԴg4׉I^@pg#nK$$T8%۳oqO6dkalU{ 4W\_t^sfV"[a2%Qsed) u)t69͢[ar䐨Aw-(W|Pj=+KzjX|)_qy1`&:Y {zBn"S擖K%pIu`4^zdp(1v3nF59T͎3R A,E 8rqJZ7s[)~7;RԎ£kA@EAfsL! ȵ \ \`X%gȮi>|{p34Qgf;2ip!PF %`Z7fe12& a=g";m=\kl]W\oj/PL'7"qF }D&𺪊зyM)*:W7n5Y\!_~0JςJs$ \̑wm8 o앞 q KAkȥDe(G@y &mMgC+e"q-CD5 V>L#yKQϊێt>EjEbmn|>uOO#Tf1_HcN?62qOt؆2j!rPK!)udrs/downrev.xmlDj0DB/C n`BC{ $-ummke$%v=a7fƱ,A\9mQ{^Yc(f}\t=F$1jb8ucඓ,{ {ڶT?[AC1-wPa,^AD)/E}h F0D [2M ?PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!b~*drs/shapexml.xmlPK-!)uDdrs/downrev.xmlPKG }j  0F>___PPT9  $ !", MINLP "   L   0e0e ?!>45@68<>5 2" ù PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!cS`Ydrs/shapexml.xml[n6;Y;^ψH-`,8 Zc5RɩK}ݢ>I_3hKnk;`>~3B22 bWuJ~ nVo%\Q;U("-QN3EP]QcS8%g>nށf#?#LUW݅|YY¸޲A؈6p||"ڥ^8ƒ@A)ηֳ6[pjEvp( as|U!yc*K&ZyIaM MBrLf-`+o>8!kī|k%?Vi,DYlL1b[(x3b/:,iXS +Gnkٷyt woI"nȚ˶zy顨B~JGc|YgK 3ohDd;2@ 8AB>G=8:>2 ?>:07K205B: 7040G8 MINLP 8 <5B>4K 8E @5H5=8O 0:B82=> 87CG0NBAO ?>A;54=85 30-40 ;5B; =0 =0AB>OI89 <><5=B MB> 2A5 5I5 0:BC0;L=0O >1;0ABL, ?5@A?5:B82=0O A B>G:8 7@5=8O ?>;CG5=8O =>2KE @57C;LB0B>2; 2 D>@<5 MINLP :0: ?@028;> AB02OBAO 7040G8, 2 :>B>@KE B@51C5BAO >4=>2@5<5==> >?B8<878@>20BL AB@C:BC@C A8AB5<K (48A:@5B=0O G0ABL) 8 55 ?0@0<5B@K (=5?@5@K2=0O G0ABL); >;;5:F8O 7040G 2 D>@<5 MINLP: I.E. Grossmann and N.V. Sahinidis (eds) (2002). Special Issue on Mixed-integer Programming and it s Application to Engineering, PartI, Optim. Eng., 3(4), Kluwer Academic Publishers, Netherlands. I.E. Grossmann and N.V. Sahinidis (eds) (2002). Special Issue on Mixed-integer Programming and it s Application to Engineering, PartI, Optim. Eng., 4(1), Kluwer Academic Publishers, Netherlands. PZ P P Phpp p!"  : m    @` I}OPMk     (     ` ?03>;>2>: 1"[UPK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!39ndrs/shapexml.xmlUn@#B!VT8DUԴg4׉I^@pg#nK$$T8%۳oqO6dkalU{ 4W\_t^sfV"[a2%Qsed) u)t69͢[ar䐨Aw-(W|Pj=+KzjX|)_qy1`&:Y {zBn"S擖K%pIu`4^zdp(1v3nF59T͎3R A,E 8rqJZ7s[)~7;RԎ£kA@EAfsL! ȵ \ \`X%gȮi>|{p34Qgf;2ip!PF %`Z7fe12& a=g";m=\kl]W\oj/PL'7"qF }D&𺪊зyM)*:W7n5Y\!_~0JςJs$ \̑wm8 o앞 q KAkȥDe(G@y &mMgC+e"q-CD5 V>L#yKQϊێt>EjEbmn]{5goչo:?^]*!l_4~vW%e7B;PK!;I&drs/downrev.xmlDKk@ܔ:EQBTӠk恙3S;t.zPfV%vF;yXJ#P>EM6ܗ )ScIǮ2Na\:#\u|$\aC*`OpQqvBL X!wE틿ŵ>ݢiPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!39n*drs/shapexml.xmlPK-!;I&Fdrs/downrev.xmlPKJ }j  0F>___PPT9  6!" 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A;8 @5H5=85 48A:@5B=> ?> A>>B2. ?5@5<5==K<  !". =0G5 ?> k=1,& ,n 2KG8A;O5< ?@8@0I5=8O DC=:F88 03@0=60 ?> :064>9 ?5@5<5==>9 DL=|L(xk,l)  L(x,l)|, 345 l 8 x  <=>68B5;8 03@0=60 8 >?B8<C<K =5?@5@K2=>9 7040G8, xk  >:@C3;5==0O 225@E : 1;8609H5<C 48A:@. 7=0G5=8N k-O :>>@48=0B0 E. :@C3;O5< xk, :>B>@0O <8=8<878@C5B DL, n=n-1, (03 2. ;>E0O AE>48<>ABL ?@8 ACI5AB25==>9 =5;8=59=>AB8; A8;L=> @07@565==>9 A5B:5 2>7<>6=KE 7=0G5=89. ?B8<C< 2 8AE>4=>9 7040G5 =5>1O70B5;L=> 2 >:@5AB=>AB8 >?B8<C<0 =5?@5@K2=>9 7040G8.J Z Z ZH ZS ZJzC N 1 )Z   Z ;   5 3    7 , T@` I}OPMy___PPT10Y+D=' = @B + d(  d  d  `` ?03>;>2>: 1"d^PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!, drs/shapexml.xmlVn0G,ߢ?A6ipQMպ]:vd;݋@H|vmTBH;?᪔l)-`ϙP 5+ά#J|-,??}rPEbPV6b~\z6%]] ^MIW3UFX98*eoJ*ÔZΪTzVd1r͇ͧ~fk=B0.lLDwH`ү z!.2ꊹu\uhor8z#b#΀E!l:z|@Q/m`|xШCpF*RPp>ΣgIfn-z]Vxp(Lb.q[ Hs4,%{{}H cdV(L Uˆ9`Z7fUcU:M[ |$E-ۉA{N='\I=%O D%K8-:q.(u@cnKL7{bIs8+o]Y8[W&0,$b ՠ{dq#ބkBV+=5Z ց;`ߢV!pZ1\ҭme})"uBDLK~CS8;yk bjbx?|>MuJ$D-Hz<*!znVYEPK!Idrs/downrev.xmlDMk@E nJB$u Ԣg%`fjb~Cuys9u[v#5 JejߧXh$֐;X^_Kۙݎf bB]y(&֑I]eƘ%n,\2AGʟvvYPW az BG},R%/)`ݯ^H^@rKPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!, *drs/shapexml.xmlPK-!IQdrs/downrev.xmlPKS }j  0F>___PPT9  8" "   & (BBM)&  , 3 d  0e0e ?!>45@68<>5 2" PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!ΓTu7drs/shapexml.xml[n6w x;N\7?F" mQq^LZ$J#)U 밋a=^aII2xN !ux>~Y)*JE@wmSE"qЋW[(Ĉũኾ<ì2BuNκ 'xQ tҘa8EZ$W,ӕ+N-%o%ʨ)*;նyFE{'ill@1k@uY<ըat&=1B#h֒Igö)b`2nش1k]֌(ǹNǑ&l̽ii-3"Vzob~_A(sY$1a^10jgVDC$F@@J _a1%#>>gvEʠzD^[0Ʃv-$n 0qE8L5z* &Sfp5&-mZ8RV+'[ bEXߕ,'\;Oc077~da;8Rjn+J+,蛌Y4Jma'0IB|~v nc]X2l}[٥viލ[?Wpm|<|8uU𷨗q13WeϪ rֽl)QҷIJMT(,HMKLNUMMH$I$$ZR Y`URᔟR fPK!1@3drs/downrev.xmlDMO0DHkQ"*t[J@m9p\Gבmcq(ь-Vԉ}h O2P,3T$:'pՂrik rBhbsCٰ0q=K*-}!mY6ӖZI iXM=̼xA?=x{3@Ex[?R z=(D-&K_PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!ΓTu7*drs/shapexml.xmlPK-!1@3drs/downrev.xmlPK v 0RJ___PPT9,$ f5:>B>@K5 >?@545;5=8O (Reinschmidt, 1971) Half-bandwidth: <>6=> @5H8BL =5?@5@K2=CN 7040GC, ?>A;5 G53> @0AA<>B@5BL 48A:@5B=CN >:@5AB=>ABL @5H5=8O ?> :064>9 48A:@5B=>9 :>>@48=0B5 87 55 2>7<>6=KE 7=0G5=89  r 7=0G5=89, 1>;LH8E =5?@5@K2=>3> >?B8<C<0 8 r  <5=LH8E. r  half-bandwidth. Completion: ?@8A20820=85 48A:@5B=KE 7=0G5=89 :064>9 87 48A:@5B=KE ?5@5<5==KE. Feasible completion: completion, C4>2;5B2>@ONI55 >3@0=8G5=8O<. Partial solution: ?@8A20820=85 48A:@5B=KE 7=0G5=89 ;8HL G0AB8 48A:@5B=KE ?5@5<5==KE. Fathoming: >B1@0:>2:0 =5?5@A?5:B82=KE G0AB8G=KE @5H5=89.* Z  Z* D,E /$  *    B   C  -@` I}OPM 4,h(  h  h  ` ?03>;>2>: 1"d^PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!, drs/shapexml.xmlVn0G,ߢ?A6ipQMպ]:vd;݋@H|vmTBH;?᪔l)-`ϙP 5+ά#J|-,??}rPEbPV6b~\z6%]] ^MIW3UFX98*eoJ*ÔZΪTzVd1r͇ͧ~fk=B0.lLDwH`ү z!.2ꊹu\uhor8z#b#΀E!l:z|@Q/m`|xШCpF*RPp>ΣgIfn-z]Vxp(Lb.q[ Hs4,%{{}H cdV(L Uˆ9`Z7fUcU:M[ |$E-ۉA{N='\I=%O D%K8-:q.(u@cnKL7{bIs8+o]Y8[W&0,$b ՠ{dq#ބkBV+=5Z ց;`ߢV!pZ1\ҭme})"uBDLK~CS8;yk bjbx?|>MuJ$D-Hz<*!znVYEPK!Idrs/downrev.xmlDMk@E nJB$u Ԣg%`fjb~Cuys9u[v#5 JejߧXh$֐;X^_Kۙݎf bB]y(&֑I]eƘ%n,\2AGʟvvYPW az BG},R%/)`ݯ^H^@rKPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!, *drs/shapexml.xmlPK-!IQdrs/downrev.xmlPKS }j  0F>___PPT9  8" "   & (BBM)&  ,  h  0e0e ?!>45@68<>5 2": 4 PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!rh:drs/shapexml.xmlZn6w x;v'(E 0 hHFRao=:b3xOW9dI^Wm-!yx>~1>~JbJG .%Btۀ^_]=D&,Nɗ_g#,( ˜lh OLH S0UuɔBf`$ݣN"IO`*f%|9Q$Xr/Wuw"=)HS~ iKhC"ӯhXJ$f }Δ{h4PmNM*TɻyrFi\p>v X¡0CJ8Hsm:ղY{='@ ~{s2E(yXV%RtVN(QYGy#:IԔs5IXN3LiszTF6e XgJGJ8§IȐ0fY gr;DǸȥ5օOaZg?#fjc񮶴{kD=؄q@{AvKkx 慆H΁+%X| ;)ͦ*6gƒ:CL̗E7 Y0y ԛ"%kMTOg| Y2DMZڴ.q&Rh' 0>Pf[&W Pqs2)JY>}8(UD 81vT;N Ϯհ;lֽ(a#IE(`@Uwy .Hz;\EwLDɝPx^B9gq "۾JЖ2TU'< &ZFUEn7Eq4ڬJ;7D nJcyTqlW_%r/6κmu:%YޜtpD(8a'?Q`DA!$ P'Ce^= w.,%ewFPWnnvHA|k׫6 Ţp U%>}aN)7/%UFW~ѧ>|5=VX,gf)[GHcsX])rKM7&>!lRp݅=L }ko e+xoཁcn5#jU!e t)Xe,odm'Ǽ*OF n8kU,j>RC5Ab|*%5^Ti %GX:d-#{j[Mw_+ՍH>O]E w6{+ %P]=_g|GE^hqONu h˖ސ;___PPT9  \<K1>@ ?>;C?>;>AK  M2@8AB8:0. >@O4>: 2K1>@0 ?5@5<5==>9 4;O ?@8A20820=8O 48A:@5B=>3> 7=0G5=8O  M2@8AB8:0. B1@0:>2:0  M2@8AB8:0. A:;NG8B5;L=> :@8B8G=0 4;O CA?5H=>AB8/2@5<5=8 ?>8A:0. $0:B8G5A:8, BBM  @07=>284=>ABL ?5@51>@=KE <5B>4>2 2 A>G5B0=88 A> AB@>38<8 ?@028;0<8 8 M2@8AB8:0<8 4;O A>:@0I5=8O ?5@51>@0. @5<O ?>8A:0 M:A?>=5=F80;L=> 2>7@0AB05B A @>AB>< :>;8G5AB20 48A:@5B=KE ?5@5<5==KE. "5< =5 <5=55, :;0AA8G5A:89 8 25AL<0 ?>?C;O@=K9 <5B>4. :B82=> 8A?>;L7C5BAO 2 A>G5B0=88 A 4@C38<8: 3@0485=B=K<8, SQP, <5B>4 HB@0D=KE DC=:F89, SLP& $ ZI  H  "    @` I}OPM$  l(  l  l  `@ ?03>;>2>: 1"d^PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!, drs/shapexml.xmlVn0G,ߢ?A6ipQMպ]:vd;݋@H|vmTBH;?᪔l)-`ϙP 5+ά#J|-,??}rPEbPV6b~\z6%]] ^MIW3UFX98*eoJ*ÔZΪTzVd1r͇ͧ~fk=B0.lLDwH`ү z!.2ꊹu\uhor8z#b#΀E!l:z|@Q/m`|xШCpF*RPp>ΣgIfn-z]Vxp(Lb.q[ Hs4,%{{}H cdV(L Uˆ9`Z7fUcU:M[ |$E-ۉA{N='\I=%O D%K8-:q.(u@cnKL7{bIs8+o]Y8[W&0,$b ՠ{dq#ބkBV+=5Z ց;`ߢV!pZ1\ҭme})"uBDLK~CS8;yk bjbx?|>MuJ$D-Hz<*!znVYEPK!Idrs/downrev.xmlDMk@E nJB$u Ԣg%`fjb~Cuys9u[v#5 JejߧXh$֐;X^_Kۙݎf bB]y(&֑I]eƘ%n,\2AGʟvvYPW az BG},R%/)`ݯ^H^@rKPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!, *drs/shapexml.xmlPK-!IQdrs/downrev.xmlPKS }j  0F>___PPT9  8" "   & (BBM)&  , T l   0e0e ?!>45@68<>5 2 r 0 45O <5B>40: @5H05< =5?@5@K2=>5 @0AH8@5=85; if x discrete  STOP; 5A;8 xi =5 87 <=>-20 D, dij < xi < dij+1; >?@545;O5< 2 ?>47040G8  A >3@0=8G5=85< xi e" dij+1, xi d" dij.  branching. 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ց;`ߢV!pZ1\ҭme})"uBDLK~CS8;yk bjbx?|>MuJ$D-Hz<*!znVYEPK!Idrs/downrev.xmlDMk@E nJB$u Ԣg%`fjb~Cuys9u[v#5 JejߧXh$֐;X^_Kۙݎf bB]y(&֑I]eƘ%n,\2AGʟvvYPW az BG},R%/)`ݯ^H^@rKPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!, *drs/shapexml.xmlPK-!IQdrs/downrev.xmlPKS }j  0F>___PPT9  8" "   & (BBM)&  , r p  @ 0e0e ?!>45@68<>5 2 r 0 D45O <5B>40: B1@0:>2:0: 4>?CAB8<>5 48A:@5B=>5 @5H5=85 8<55B EC4H55 7=0G5=85 DC=:F88 AB>8<>AB8, G5< B5:CI0O 25@E=OO >F5=:0; =5A>2<5AB=0O =5?@5@K2=0O 7040G0; >?B8<C< =5?@5@K2=>9 7040G8 EC65 G5< B5:CI0O 25@E=OO >F5=:0. @>F5AA 7025@H05BAO, :>340 =5 >AB05BAO C7;>2 2 45@525. 0E>645=85 3;>10;L=>3> >?B8<C<0 30@0=B8@C5BAO B>;L:> 4;O ;8=59=>9 8;8 2K?C:;>9 7040G8. 0<5G0=85: @5H5=85 =5?@5@K2=>9 7040G8 405B =86=NN >F5=:C.          `2    a   /  ` I}OPM7   @t (  t  t  ``  ?03>;>2>: 1"e_PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ 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Leyffer, The University of Dundee SBB Branch-and-Bound algorithm from ARKI Consulting and Development =>3> <0B5@80;>2 A> A@02=5=85< A>;25@>2: Leyffer, Grossmann 8 4@C385 02B>@K. 01>B0 Leyffer 40B8@>20=0 09, 2008. !>;25@ filMINTD P PN4F  V  Y  P  r   O  W  @ (    nplqrt &vxzNQ @` I}OPM (     `g ?03>;>2>: 1"icPK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!I/' drs/shapexml.xmlVn0G,ߢ?A6ipQMպ]OfuvJ5܁3ۨ QqϏxUHZż{LD3H$1_ ˏϟ-ʘϝ+v&sQ=ХPep4viʑEl:vACRI96^J.c4=raqymO~a]nk?NAD(5i) pA;!S/-̭Kr*ޠ?8|X[a"ۭNuQ44>4琱6H%b>)Tr:˝ǵѫuwoG\vBPQ]2r);W)'$ghVY*+N61t܌ԩYJL+w\Tp&фQeNj>W*AnMIxLLƉcKBnBAS=:F;ΤZZds'#18/.E`2Ɖ"t,uQyoRdsS.1`ϋMkó~M@+= g as$Q \}ϑ7]8N {F,in:HpgRv=ls)ґ*ej"ݪT>Y&cʇia3JEqےGHОBPH"{!a=g] IAj]OG){ ޤ6_<{Ú*,~PK!rqh]drs/downrev.xmlDMK1E!L'ko95vIg ̵yK]EpQA˥ eC:U)Zj}NβVl9=4衡km]5>|~./D!_>_ƛ@TOoC$ %d rPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!I/' *drs/shapexml.xmlPK-!rqh]Sdrs/downrev.xmlPKX }j  0F>___PPT9  !" S. LEYFFER "  m   p0e0e ?!>45@68<>5 2"{ u PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!;.ZQ>drs/shapexml.xml[n6w x;v'Y(E![0h5SFRbo>C;b3xOW9[nM-u!:ۋ43=h܅ XD[5p8AIK6A9%bo@J5a 'P+8ɔ X1|īCn=Sؒ9CvdNqӚOK=ORIYwtU<,q'cw.PjM5.G7<,"9 낧,xDp28i+ڗZ6 ths辬_Yg) FkϽˈJAD̀F.EɌkO@5 tоn.;f RK'.er{&8N;uD֥:τKYw.j97x*rdYb7UڙךؿeKX/]6*8٨+-Ma3ų@Y1Tf1Ne&#șf 6]RHYGI?lbXW< ]X .~ nfz3i@A]*am7xvU¶=Cdo.7".Aţ߹Lvj(ްC62 4>#JaVf\/\Y)ٮTn uU;EM4CԮ%J 2I:-mM`wn6l[$.hy+ !huE؊Jۀg|$w!JkLM֟/BH:2A*5-ӁqF*1 6Tʹ?ºFW·dJ?izKDM'l!) ( \}[ڸwO@\2ey GE~9v@kժh|2l}s}j,c/LAz]/]@7L]U _7&Iq_ɏs T'-PK!NVdrs/downrev.xmlDMo0Dĭ8HZxAc; I}q47z͠[qek 6UK>QZ#{جV*ۛ_P1>%:.5kS۱]irGn,IRScCMok.~FQ-Ϗ<+9ax}x].V2 ܏'ר!Eh r PK!sB'=Ydrs/_rels/shapexml.xml.rels̔j1Ðs^((UV>@̜ &'!., nIȗ?wZ%t^X'mIBRŸ8\Œѳ?GC§TZ 4 jg/Yu:15E:XܝQ/Kt,iNzNԍuOF+L3ZZW6KT~Oɇ0PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!;.ZQ>*drs/shapexml.xmlPK-!NVdrs/downrev.xmlPK-!sB'=Y drs/_rels/shapexml.xml.relsPK>!  j 0F>___PPT9  "http://www-unix.mcs.anl.gov/~leyffer/research.htm 01>@ B5AB>2 4;O MINLP  B0:65: Dundee solvers for MINLP/NLP/QP MINLP solver on the NEOS server NLP solver on the NEOS server TOMLAB /MINLP, Matlab interface with sparse and dense versions of the Dundee solvers S. Leyffer. Deterministic Methods for Mixed Integer Nonlinear Programming. PhD thesis, University of Dundee, Dundee, Scotland, UK, 1993. 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LeyfferКорифеи *Использованные шрифты Тема(Внедренные серверы OLE"Заголовки слайдов* 8@ _PID_HLINKSA mailto:itlab.vlsi@cs.vmk.unn.ru http://www.gamsworld.org/minlp/,http://www.gamsworld.org/minlp/minlplib.htm.http://www-unix.mcs.anl.gov/leyffer/macminlp+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm2http://www-unix.mcs.anl.gov/~leyffer/research.htm2http://www-unix.mcs.anl.gov/~leyffer/solvers.html;http://www-neos.mcs.anl.gov/neos/solvers/MINCO:MINLP-AMPL/:http://www-neos.mcs.anl.gov/neos/solvers/NCO:FILTER-AMPL/"http://tomlab.biz/products/minlp/"http://tomlab.biz/products/minlp/"http://tomlab.biz/products/minlp/ mailto:itlab.vlsi@cs.vmk.unn.ru http://www.gamsworld.org/minlp/,http://www.gamsworld.org/minlp/minlplib.htm.http://www-unix.mcs.anl.gov/leyffer/macminlp+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm2http://www-unix.mcs.anl.gov/~leyffer/research.htm2http://www-unix.mcs.anl.gov/~leyffer/solvers.html;http://www-neos.mcs.anl.gov/neos/solvers/MINCO:MINLP-AMPL/:http://www-neos.mcs.anl.gov/neos/solvers/NCO:FILTER-AMPL/"http://tomlab.biz/products/minlp/ _ meyerovimeyerovi  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrsuvwxyz{|}~ Root EntrydO)Pictures!Current UserSummaryInformation(tPowerPoint Document( DocumentSummaryInformation8Root EntrydO)^HPictures!Current UserSummaryInformation(t$           ! " # ՜.+,D՜.+,    ( 0 Экран (4:3)$State University of Nizhni Novgorod%* 7ArialGeorgia Wingdings Wingdings 2Calibri Эркер 1_Эркер 2_Эркер 3_Эркер 4_Эркер 5_Эркер 6_ЭркерФормулаСмешанные нелинейные задачи оптимизации: постановки и методы решенияИсточникиСодержаниеJСмешанные задачи. Немного терминологии Смешанные задачиАктуальность MINLPПрименимость MINLP,Постановка задачи MINLP (1),Постановка задачи MINLP (2)О сложности MINLP9Немного о построении моделей…9Немного о построении моделей…"Методы решения MINLP(Округление (Rounding-off) …(Округление (Rounding-off) …1Метод ветвей и границ (BBM)…1Метод ветвей и границ (BBM)…1Метод ветвей и границ (BBM)…1Метод ветвей и границ (BBM)….Метод ветвей и границ (BBM)KПоследовательная линеаризация (SLP) и SQP…HПоследовательная линеаризация (SLP) и SQP.Гибридный алгоритм SQP & BBM.Метод штрафных функций….Метод штрафных функций…+Метод штрафных функций1Метод множителей ЛагранжаCМетод имитации отжига (Simulated annealing)…CМетод имитации отжига (Simulated annealing)…@Метод имитации отжига (Simulated annealing)>Генетический алгоритм (Genetic algorithm)'Другие методы (OA, GBD)…$Другие методы (OA, GBD)'Подзадачи Outer Approximation OA vs GBDBРазвитие OA – LP/NLP-based branch and bound (LP/NLP-BB) LP/NLP-BBДругие методы (CP)СолверыСолверыСайт S. LeyfferКорифеи *Использованные шрифты Тема(Внедренные серверы OLE"Заголовки слайдов* 8@ _PID_HLINKSA mailto:itlab.vlsi@cs.vmk.unn.ru http://www.gamsworld.org/minlp/,http://www.gamsworld.org/minlp/minlplib.htm.http://www-unix.mcs.anl.gov/leyffer/macminlp+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm2http://www-unix.mcs.anl.gov/~leyffer/research.htm2http://www-unix.mcs.anl.gov/~leyffer/solvers.html;http://www-neos.mcs.anl.gov/neos/solvers/MINCO:MINLP-AMPL/:http://www-neos.mcs.anl.gov/neos/solvers/NCO:FILTER-AMPL/"http://tomlab.biz/products/minlp/"http://tomlab.biz/products/minlp/"http://tomlab.biz/products/minlp/ mailto:itlab.vlsi@cs.vmk.unn.ru http://www.gamsworld.org/minlp/,http://www.gamsworld.org/minlp/minlplib.htm.http://www-unix.mcs.anl.gov/leyffer/macminlp+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm+http://www.gamsworld.org/minlp/solvers.htm2http://www-unix.mcs.anl.gov/~leyffer/research.htm2http://www-unix.mcs.anl.gov/~leyffer/solvers.html;http://www-neos.mcs.anl.gov/neos/solvers/MINCO:MINLP-AMPL/:http://www-neos.mcs.anl.gov/neos/solvers/NCO:FILTER-AMPL/"http://tomlab.biz/products/minlp/PowerPoint Document( DocumentSummaryInformation8