param N integer := 378; param M integer := 16; param A{1..M,1..M}; param B{1..M,1..2}; param C{1..2,1..M}; param D{1..2,1..2}; set I = 1 .. N; set J = N..2*N-1; param Nu integer := 189; param a1{1..Nu}; param a2{1..Nu}; param k{i in 1..Nu} := i; param mx := .01; param my := .008; param pi := 4*atan(1); param alp :=exp(-15/75); param pn{i in 0..N-1} := i*2*pi/N; var alpha{1..Nu,1..2} := Uniform(-pi,pi); var x{i in 0..N-1,j in 1..2} := 1; var z{i in 0..N,j in 1..M} := 1; var y{i in 0..2*N-1, j in 1..2} := 1; var t; param bd := .0085; minimize obj: t; s.t. bound31{j in N..2*N-1}: -t*sqrt((1/N)*sum{i in N..2*N-1}y[i,1]^2)<=y[j,1]; s.t. bound32{j in N..2*N-1}: y[j,1]<= t*sqrt((1/N)*sum{i in N..2*N-1}y[i,1]^2); s.t. bound41{j in N..2*N-1}: -t*sqrt((1/N)*sum{i in N..2*N-1}y[i,2]^2)<=y[j,2]; s.t. bound42{j in N..2*N-1}: y[j,2]<= t*sqrt((1/N)*sum{i in N..2*N-1}y[i,2]^2); s.t. bound51{j in N..2*N-1}: y[j,1]<= bd; s.t. bound52{j in N..2*N-1}: -bd <= y[j,1]; s.t. bound61{j in N..2*N-1}: y[j,2]<= bd; s.t. bound62{j in N..2*N-1}: -bd <= y[j,2]; s.t. inp{i in 0..N-1, j in 1..2}: x[i,j]= if j==1 then sum{u in 1..Nu}(a1[u]*cos(pn[i]*k[u]+alpha[u,j])) else sum{u in 1..Nu}(a2[u]*cos(pn[i]*k[u]+alpha[u,j])); s.t. out1{i in 1..N,j in 1..M}: z[i,j]=sum{l in 1..M}A[j,l]*z[i-1,l] + sum{l in 1..2}B[j,l]*x[i-1,l]; s.t. out2{i in 1..N,j in 1..2}: y[i,j]=sum{l in 1..M}C[j,l]*z[i,l]; s.t. out3{i in N+1..2*N-1,j in 1..2}: y[i,j]=sum{l in 1..M}C[j,l]*z[i-N-1,l]; s.t. move1{i in 0..N-2, j in 1..2}: -mx <= x[i+1,j] - x[i,j] <= mx; s.t. move2{j in 1..2}: -mx <= x[0,j]-x[N-1,j] <= mx; s.t. movey{i in N-1..2*N-2, j in 1..2}: -my <= y[i+1,j] - y[i,j] <= my; data; param a1 := 1 0.00022289087552464083 2 0.00000000000000000275 3 0.00334336313490998530 4 0.00022289087504879414 5 0.00000000000000000083 6 0.00334336318415442160 7 0.00022289087464499898 8 0.00000000000000000947 9 0.00334336313522526740 10 0.00022289087464766086 11 0.00000000000000000684 12 0.00334336314729334830 13 0.00022289094805541017 14 0.00000000000000000853 15 0.00334336313491902150 16 0.00022289089697191181 17 0.00000000000000000644 18 0.00334336324823089270 19 0.00022289088290535657 20 0.00000000000000001155 21 0.00334336317946100190 22 0.00022289087518256726 23 0.00000000000000001258 24 0.00334336345597006840 25 0.00022289091642486080 26 0.00000000000000002096 27 0.00334336333126951120 28 0.00022289087543975978 29 0.00000000000000001583 30 0.00334336317076692820 31 0.00022289094407285017 32 0.00000000000000002540 33 0.00334336351580412400 34 0.00022289101138375523 35 0.00000000000000001363 36 0.00334336311992510220 37 0.00022289106134404740 38 0.00000000000000000597 39 0.00334336311954237580 40 0.00022289088040704249 41 0.00000000000000001190 42 0.00334336313456668660 43 0.00022289089368341522 44 0.00000000000000001415 45 0.00334336315721651300 46 0.00022289090719604051 47 0.00000000000000002637 48 0.00334336404549133090 49 0.00022289186828479811 50 0.00000000000000001154 51 0.00033433636726042657 52 0.00002228910182994871 53 0.00000000000000000743 54 0.00033433646606497765 55 0.00002228924995453296 56 0.00000000000000000953 57 0.00033433633188684647 58 0.00002228910103402672 59 0.00000000000000001126 60 0.00033433631330756009 61 0.00002228915059104206 62 0.00000000000000001304 63 0.00033433633573039831 64 0.00002229050130972427 65 0.00000000000000000909 66 0.00033433701746375221 67 0.00002228936916823548 68 0.00000000000000000251 69 0.00033433699772647763 70 0.00002229026642942421 71 0.00000000000000000706 72 0.00033433644483010110 73 0.00002228913611574275 74 0.00000000000000000390 75 0.00033434228415983759 76 0.00002228971443037848 77 0.00000000000000001230 78 0.00033433635458217066 79 0.00002228924364521896 80 0.00000000000000000231 81 0.00033433647487767052 82 0.00002229081934496241 83 0.00000000000000000520 84 0.00033433643824780899 85 0.00002228934736615575 86 0.00000000000000000829 87 0.00033433632314304354 88 0.00002228979068946210 89 0.00000000000000000386 90 0.00033433637591279299 91 0.00002228911396124466 92 0.00000000000000000128 93 0.00033433640392419625 94 0.00002229400112171797 95 0.00000000000000000383 96 0.00033433686514784114 97 0.00002228914862989695 98 0.00000000000000000712 99 0.00033433641078901621 100 0.00002228922087155455 101 0.00000000000000000878 102 0.00033433631577118065 103 0.00002228936126977457 104 0.00000000000000000977 105 0.00033433633255095462 106 0.00002228924163617376 107 0.00000000000000000282 108 0.00033433635055279059 109 0.00002228910874700237 110 0.00000000000000000737 111 0.00033433652109604898 112 0.00002229007801441896 113 0.00000000000000000589 114 0.00033433713149281857 115 0.00002228909992101418 116 0.00000000000000000523 117 0.00033433648125539395 118 0.00002228964301200296 119 0.00000000000000000281 120 0.00033433644670094746 121 0.00002229284398892141 122 0.00000000000000000233 123 0.00033433879592043681 124 0.00002229078634830502 125 0.00000000000000000114 126 0.00033433658301370146 127 0.00002228908770611206 128 0.00000000000000000146 129 0.00033433631880765564 130 0.00002229681811884333 131 0.00000000000000001057 132 0.00033433632481261194 133 0.00002228908752040533 134 0.00000000000000000045 135 0.00033433693577309098 136 0.00002229272328563321 137 0.00000000000000000542 138 0.00033433650347494215 139 0.00002229205309769029 140 0.00000000000000000578 141 0.00033433632349740428 142 0.00002228931405990040 143 0.00000000000000000912 144 0.00033433631220501614 145 0.00002230843473290219 146 0.00000000000000001646 147 0.00033434951215665054 148 0.00002228911538382363 149 0.00000000000000000704 150 0.00033433632085515914 151 0.00002228919604250863 152 0.00000000000000001720 153 0.00033433787430083868 154 0.00002229106953520624 155 0.00000000000000000560 156 0.00033433665395290790 157 0.00002228910249626877 158 0.00000000000000001251 159 0.00033433636903654678 160 0.00002229100280743955 161 0.00000000000000001523 162 0.00033433641993354732 163 0.00002228909331079480 164 0.00000000000000000967 165 0.00033433685435970876 166 0.00002230728256407887 167 0.00000000000000001302 168 0.00033433640491411582 169 0.00002229105519162734 170 0.00000000000000001158 171 0.00033433631576334529 172 0.00002228910241495257 173 0.00000000000000001555 174 0.00033433680539813167 175 0.00002229181649788271 176 0.00000000000000000302 177 0.00033433741677380322 178 0.00002229180554313700 179 0.00000000000000000630 180 0.00033434472857700844 181 0.00002228983745674525 182 0.00000000000000001000 183 0.00033434686574844777 184 0.00002228934697598421 185 0.00000000000000000297 186 0.00033434012098512673 187 0.00002228975893009189 188 0.00000000000000000277 189 0.00033434012098512673 ; param a2 := 1 0.00000000000000000236 2 0.00022289087473891713 3 0.00334336313228354980 4 0.00000000000000000754 5 0.00022289087501907510 6 0.00334336317265312640 7 0.00000000000000000376 8 0.00022289087690666214 9 0.00334336313178483590 10 0.00000000000000000520 11 0.00022289087488235545 12 0.00334336314414549700 13 0.00000000000000000882 14 0.00022289088561553431 15 0.00334336313342773390 16 0.00000000000000000502 17 0.00022289089552283853 18 0.00334336320235863750 19 0.00000000000000000368 20 0.00022289089441480063 21 0.00334336313910478310 22 0.00000000000000001708 23 0.00022289087637685265 24 0.00334336335621001570 25 0.00000000000000000594 26 0.00022289087592872726 27 0.00334336325780265230 28 0.00000000000000001097 29 0.00022289105787339075 30 0.00334336318849104160 31 0.00000000000000000750 32 0.00022289115982685023 33 0.00334336350372920230 34 0.00000000000000002745 35 0.00022289088490996391 36 0.00334336313521832550 37 0.00000000000000002792 38 0.00022289093045980694 39 0.00334336312026575420 40 0.00000000000000001228 41 0.00022289096479364727 42 0.00334336312548698040 43 0.00000000000000000807 44 0.00022289135257381939 45 0.00334336313946503520 46 0.00000000000000001064 47 0.00022289087518222433 48 0.00334336367731065880 49 0.00000000000000001213 50 0.00022289094203785267 51 0.00033433631525194756 52 0.00000000000000000887 53 0.00002228909612550775 54 0.00033433650640441939 55 0.00000000000000000276 56 0.00002228908795692516 57 0.00033433633270297034 58 0.00000000000000000421 59 0.00002228918257553508 60 0.00033433631953778763 61 0.00000000000000000682 62 0.00002229101909800414 63 0.00033433632733553185 64 0.00000000000000000993 65 0.00002228908748744945 66 0.00033433694973131970 67 0.00000000000000000653 68 0.00002228908778886751 69 0.00033433635155667550 70 0.00000000000000000544 71 0.00002228915827359569 72 0.00033433633818124475 73 0.00000000000000000156 74 0.00002228970342811877 75 0.00033434085675404090 76 0.00000000000000000393 77 0.00002228908771537361 78 0.00033433636421075381 79 0.00000000000000001265 80 0.00002228908765622120 81 0.00033433634738233331 82 0.00000000000000000253 83 0.00002228909833426848 84 0.00033433633090815105 85 0.00000000000000000440 86 0.00002228947517003175 87 0.00033433631445948245 88 0.00000000000000001452 89 0.00002228929454185607 90 0.00033433632023096703 91 0.00000000000000000309 92 0.00002228909018426212 93 0.00033433632615093489 94 0.00000000000000000942 95 0.00002228924358889593 96 0.00033433649021460661 97 0.00000000000000001022 98 0.00002228915339902778 99 0.00033433638219238838 100 0.00000000000000001019 101 0.00002228909902840758 102 0.00033433641884491314 103 0.00000000000000000676 104 0.00002228942227987566 105 0.00033433633434734058 106 0.00000000000000001077 107 0.00002228933554061457 108 0.00033433633843310431 109 0.00000000000000000626 110 0.00002228947598219941 111 0.00033433646243077815 112 0.00000000000000000581 113 0.00002228913008157989 114 0.00033433743769988961 115 0.00000000000000001286 116 0.00002228910692145255 117 0.00033433652904784564 118 0.00000000000000000960 119 0.00002228910931469305 120 0.00033433689800263831 121 0.00000000000000000367 122 0.00002229003098097036 123 0.00033433684467000795 124 0.00000000000000000489 125 0.00002229010837101799 126 0.00033433631430438207 127 0.00000000000000000865 128 0.00002229053370160810 129 0.00033433645261208889 130 0.00000000000000000337 131 0.00002228915206227019 132 0.00033433634889528421 133 0.00000000000000000764 134 0.00002229092843848121 135 0.00033433666725546927 136 0.00000000000000000427 137 0.00002228948451724057 138 0.00033433631898887862 139 0.00000000000000000715 140 0.00002228930249254768 141 0.00033433632989232268 142 0.00000000000000000409 143 0.00002228986171891145 144 0.00033433634878060056 145 0.00000000000000001294 146 0.00002228924469421008 147 0.00033434048812034848 148 0.00000000000000000150 149 0.00002228908927204772 150 0.00033433643324754490 151 0.00000000000000000898 152 0.00002228971656042288 153 0.00033433674310079815 154 0.00000000000000001446 155 0.00002228923433511841 156 0.00033433640990541806 157 0.00000000000000002228 158 0.00002228911083695417 159 0.00033433631958706901 160 0.00000000000000001393 161 0.00002228949135466442 162 0.00033433631564133123 163 0.00000000000000001254 164 0.00002229133624733902 165 0.00033433656276908152 166 0.00000000000000000735 167 0.00002228981274139913 168 0.00033433673714686028 169 0.00000000000000000135 170 0.00002229007032144341 171 0.00033433633247804528 172 0.00000000000000001855 173 0.00002228909958666234 174 0.00033433631216137251 175 0.00000000000000000346 176 0.00002228967980440449 177 0.00033433632737203065 178 0.00000000000000000959 179 0.00002228994941255887 180 0.00033433889487011448 181 0.00000000000000001191 182 0.00002228935446897467 183 0.00033433996966708150 184 0.00000000000000001629 185 0.00002228973755457256 186 0.00033433836018398973 187 0.00000000000000001911 188 0.00002229135995700820 189 0.00033433836018398973 ; param A: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 := 1 0.357196 -0.030854 0.157110 0.088813 0.101385 0.065516 0.231658 0.021473 -0.625002 0.724682 -0.093717 0.051448 -0.177553 0.145853 -0.372191 0.333172 2 -0.018007 0.169098 0.080484 0.196622 0.071761 0.182950 0.084930 0.060006 -0.525674 0.941604 -0.443662 0.463233 -0.259805 0.227782 -0.047727 -0.012565 3 1.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 4 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 5 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 6 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 7 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 8 0.000000 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 9 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 10 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 11 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 12 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 13 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000 0.000000 14 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000 15 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 16 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 ; param B: 1 2 := 1 0.000000 0.000000 2 0.000000 0.000000 3 0.000000 0.000000 4 0.000000 0.000000 5 0.000000 0.000000 6 0.000000 0.000000 7 0.000000 0.000000 8 0.000000 0.000000 9 1.000000 0.000000 10 0.000000 1.000000 11 0.000000 0.000000 12 0.000000 0.000000 13 0.000000 0.000000 14 0.000000 0.000000 15 0.000000 0.000000 16 0.000000 0.000000 ; param C : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 := 1 0.357196 -0.030854 0.157110 0.088813 0.101385 0.065516 0.231658 0.021473 -0.625002 0.724682 -0.093717 0.051448 -0.177553 0.145853 -0.372191 0.333172 2 -0.018007 0.169098 0.080484 0.196622 0.071761 0.182950 0.084930 0.060006 -0.525674 0.941604 -0.443662 0.463233 -0.259805 0.227782 -0.047727 -0.012565 ; param D: 1 2 := 1 0.000000 0.000000 2 0.000000 0.000000 ;