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 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; minimize obj: t; s.t. bound11{j in 0..N-1}: -t*sqrt((1/N)*sum{i in 0..N-1}x[i,1]^2)<=x[j,1]; s.t. bound12{j in 0..N-1}: x[j,1]<= t*sqrt((1/N)*sum{i in 0..N-1}x[i,1]^2); s.t. bound21{j in 0..N-1}: -t*sqrt((1/N)*sum{i in 0..N-1}x[i,2]^2)<=x[j,2]; s.t. bound22{j in 0..N-1}: x[j,2]<= t*sqrt((1/N)*sum{i in 0..N-1}x[i,2]^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]; data; param a1 := 1 0.00045452829534860950 2 0.00000000000000000288 3 0.00045452940270056491 4 0.00000000000000000096 5 0.00045452792630245405 6 0.00000000000000000386 7 0.00045452954431069137 8 0.00000000000000000167 9 0.00045452870115230434 10 0.00000000000000000252 11 0.00045452918959028733 12 0.00000000000000000049 13 0.00045453162458227239 14 0.00000000000000000287 15 0.00045452962113251121 16 0.00000000000000000226 17 0.00045453056317636408 18 0.00000000000000000209 19 0.00045452895969679198 20 0.00000000000000000239 21 0.00045452863112887328 22 0.00000000000000000511 23 0.00045452866750885233 24 0.00000000000000000171 25 0.00045452896970154340 26 0.00000000000000000141 27 0.00045452939249104245 28 0.00000000000000000084 29 0.00045452910916738093 30 0.00000000000000000261 31 0.00045452962760025292 32 0.00000000000000000511 33 0.00045452901290518724 34 0.00000000000000000174 35 0.00045452806982969313 36 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0.00004545560317960542 150 0.00000000000000000280 151 0.00004545654526411508 152 0.00000000000000000207 153 0.00004545400621349670 154 0.00000000000000000091 155 0.00004545293025946318 156 0.00000000000000000595 157 0.00004544517326722589 158 0.00000000000000000096 159 0.00004545277962299613 160 0.00000000000000000252 161 0.00004545032704428941 162 0.00000000000000000215 163 0.00004544154489428287 164 0.00000000000000000409 165 0.00004545231988627839 166 0.00000000000000000449 167 0.00004546755866692796 168 0.00000000000000000331 169 0.00004544706388346667 170 0.00000000000000000349 171 0.00004545394704951724 172 0.00000000000000000065 173 0.00004551703745523879 174 0.00000000000000000127 175 0.00004545179308559544 176 0.00000000000000000107 177 0.00004545289164042382 178 0.00000000000000000309 179 0.00004545068139868460 180 0.00000000000000000343 181 0.00004545838035527208 182 0.00000000000000000193 183 0.00004545322172025351 184 0.00000000000000000287 185 0.00004545788501601743 186 0.00000000000000000204 187 0.00004544793328347791 188 0.00000000000000000229 189 0.00004544793328347791 ; param a2 := 1 0.00000000000000000373 2 0.00045460668066715039 3 0.00000000000000000390 4 0.00045460665952822780 5 0.00000000000000000319 6 0.00045460666288902587 7 0.00000000000000000254 8 0.00045460666263060943 9 0.00000000000000000284 10 0.00045460666457721664 11 0.00000000000000000111 12 0.00045460666471686773 13 0.00000000000000000346 14 0.00045460666407158313 15 0.00000000000000000271 16 0.00045460666075507655 17 0.00000000000000000424 18 0.00045460667243633581 19 0.00000000000000000663 20 0.00045460666076125781 21 0.00000000000000000244 22 0.00045460666597376423 23 0.00000000000000000284 24 0.00045460667508853252 25 0.00000000000000000295 26 0.00045460665950576410 27 0.00000000000000000080 28 0.00045460667468147863 29 0.00000000000000000201 30 0.00045460666036237695 31 0.00000000000000000195 32 0.00045460666656544171 33 0.00000000000000000479 34 0.00045460667631084888 35 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0.00000000000000000323 112 0.00004546065610340818 113 0.00000000000000000262 114 0.00004546069667312930 115 0.00000000000000000165 116 0.00004546067108775531 117 0.00000000000000000104 118 0.00004546077372266379 119 0.00000000000000000291 120 0.00004546070497695786 121 0.00000000000000000272 122 0.00004546051874697929 123 0.00000000000000000257 124 0.00004546046897039788 125 0.00000000000000000331 126 0.00004546082858031765 127 0.00000000000000000344 128 0.00004546058164278023 129 0.00000000000000000321 130 0.00004546025092770267 131 0.00000000000000000282 132 0.00004546083161902432 133 0.00000000000000000421 134 0.00004546047796431803 135 0.00000000000000000204 136 0.00004546060353894246 137 0.00000000000000000066 138 0.00004546066845827420 139 0.00000000000000000073 140 0.00004546056705320669 141 0.00000000000000000365 142 0.00004546071974976540 143 0.00000000000000000049 144 0.00004546069220245379 145 0.00000000000000000209 146 0.00004546074729130149 147 0.00000000000000000214 148 0.00004546066214416482 149 0.00000000000000000172 150 0.00004546066567015887 151 0.00000000000000000083 152 0.00004546056066574397 153 0.00000000000000000195 154 0.00004546055908543886 155 0.00000000000000000120 156 0.00004546072971459834 157 0.00000000000000000243 158 0.00004546064938961094 159 0.00000000000000000357 160 0.00004546067268062786 161 0.00000000000000000243 162 0.00004546066842006739 163 0.00000000000000000264 164 0.00004546100729528080 165 0.00000000000000000513 166 0.00004546063089721236 167 0.00000000000000000176 168 0.00004546066790256151 169 0.00000000000000000176 170 0.00004546052592912438 171 0.00000000000000000333 172 0.00004546062487180488 173 0.00000000000000000273 174 0.00004546061453543457 175 0.00000000000000000378 176 0.00004546055055386347 177 0.00000000000000000393 178 0.00004546064915677685 179 0.00000000000000000285 180 0.00004546068067049098 181 0.00000000000000000096 182 0.00004546069935834122 183 0.00000000000000000061 184 0.00004546061012575354 185 0.00000000000000000112 186 0.00004546066859028358 187 0.00000000000000000255 188 0.00004546067810902612 189 0.00000000000000000255 ; 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 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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 ;