[37] | 1 | function regress_dualize |
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| 2 | |
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| 3 | |
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| 4 | ops = sdpsettings('verbose',0); |
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| 5 | |
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| 6 | % TEST 1 |
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| 7 | yalmip('clear') |
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| 8 | A = randn(3,3);A = -A*A'; |
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| 9 | P = sdpvar(3,3); |
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| 10 | t = sdpvar(1,1); |
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| 11 | y = sdpvar(1,1); |
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| 12 | F = set(A'*P+P*A < -eye(3)); |
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| 13 | F = F + set(P > A*A') + set(P(3,3)>0) + set(t+y > 7) + set(P(2,2)>4)+set(P(1,1:2)>t) + set(t>12); |
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| 14 | obj = trace(P)+y; |
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| 15 | |
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| 16 | fail = regresstest(F,obj,ops); |
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| 17 | regressreport('Test 1',fail) |
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| 18 | |
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| 19 | % TEST 2 |
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| 20 | yalmip('clear') |
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| 21 | A = randn(3,3);A = -A*A'; |
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| 22 | P = sdpvar(3,3); |
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| 23 | t = sdpvar(1,1); |
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| 24 | y = sdpvar(1,1); |
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| 25 | F = set(A'*P+P*A < -eye(3)); |
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| 26 | F = F + set(P > 0) + set(P(3,3)>0) + set(t+y > 7) + set(P(2,2)>4)+set(P(1,1:2)>t) + set(t>12); |
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| 27 | obj = trace(P)+y; |
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| 28 | |
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| 29 | fail = regresstest(F,obj,ops); |
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| 30 | regressreport('Test 2',fail) |
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| 31 | |
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| 32 | yalmip('clear') |
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| 33 | A = randn(3,3);A = -A*A'; |
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| 34 | P = sdpvar(3,3); |
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| 35 | t = sdpvar(1,1); |
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| 36 | y = sdpvar(1,1); |
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| 37 | F = set(A'*P+P*A < -eye(3)); |
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| 38 | F = F + set(P > 0) + set(P(3,3)>0) + set(t+y > 7) + set(P(2,2)>4)+set(P(1,1:2)>t) + set(t>0); |
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| 39 | obj = trace(P)+y; |
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| 40 | |
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| 41 | fail = regresstest(F,obj,ops); |
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| 42 | regressreport('Test 3',fail) |
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| 43 | |
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| 44 | yalmip('clear') |
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| 45 | A = randn(3,3);A = -A*A'; |
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| 46 | P = sdpvar(3,3); |
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| 47 | t = sdpvar(1,1); |
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| 48 | y = sdpvar(1,1); |
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| 49 | F = set(A'*P+P*A < -eye(3)); |
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| 50 | F = F + set(P > 0) + set(P(3,3)>0) + set(t-y > 7) + set(P(2,2)>4)+set(P(1,1:2)>t) + set(t>0); |
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| 51 | obj = trace(P); |
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| 52 | |
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| 53 | fail = regresstest(F,obj,ops); |
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| 54 | regressreport('Test 4',fail) |
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| 55 | |
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| 56 | yalmip('clear') |
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| 57 | X = sdpvar(3,3); |
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| 58 | x = sdpvar(3,1); |
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| 59 | obj = trace(X)+sum(x); |
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| 60 | F = set(X>0) + set(cone(x(2:end),x(1))) + set(trace(X)==x(1)+2*x(2)+3*x(3)+4)+set(X(1,3)==8); |
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| 61 | fail = regresstest(F,obj,ops); |
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| 62 | regressreport('Test 5',fail) |
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| 63 | |
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| 64 | yalmip('clear') |
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| 65 | X = sdpvar(3,3); |
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| 66 | x = sdpvar(3,1); |
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| 67 | obj = trace(X)+sum(x); |
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| 68 | F = set(X>0) + set(cone(x(2:end),1+x(1))) + set(trace(X)==x(1)+2*x(2)+3*x(3)+4)+set(X(1,3)==8); |
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| 69 | fail = regresstest(F,obj,ops); |
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| 70 | regressreport('Test 6',fail) |
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| 71 | |
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| 72 | yalmip('clear') |
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| 73 | X = sdpvar(3,3); |
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| 74 | x = sdpvar(3,1); |
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| 75 | obj = trace(X)+sum(x); |
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| 76 | F = set(X>0) + set(cone(x(2:end),1+x(1))) + set(trace(X)==x(1)+2*x(2)+3*x(3)+4)+set(X(1,3)==8); |
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| 77 | fail = regresstest(F,obj,ops); |
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| 78 | regressreport('Test 7',fail) |
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| 79 | |
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| 80 | yalmip('clear') |
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| 81 | X = sdpvar(3,3); |
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| 82 | x = sdpvar(3,1); |
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| 83 | obj = trace(X)+sum(x); |
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| 84 | F = set(X>0) + set(cone(1-x(2:end),1+x(1))) + set(trace(X)==x(1)+2*x(2)+3*x(3)+4)+set(X(1,3)==8); |
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| 85 | fail = regresstest(F,obj,ops); |
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| 86 | regressreport('Test 8',fail) |
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| 87 | |
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| 88 | yalmip('clear') |
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| 89 | A = randn(3,3);A = -A*A'; |
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| 90 | P = sdpvar(3,3); |
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| 91 | t = sdpvar(1,1); |
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| 92 | y = sdpvar(1,1); |
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| 93 | F = set(A'*P+P*A < -eye(3)); |
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| 94 | F = F + set(P > A*A') + set(P(3,3)>0) + set(t+y > 7) + set(P(2,2)>4)+set(P(1,1:2)>t) + set(t>12)+set(t>-12); |
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| 95 | obj = trace(P)+y; |
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| 96 | fail = regresstest(F,obj,ops); |
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| 97 | regressreport('Test 9',fail) |
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| 98 | |
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| 99 | %yalmip('clear') |
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| 100 | A = randn(3,3);A = -A*A'; |
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| 101 | P = sdpvar(3,3); |
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| 102 | %t = sdpvar(1,1); |
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| 103 | %y = sdpvar(1,1); |
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| 104 | F = set(A'*P+P*A < -eye(3)); |
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| 105 | F = F + set(P > A*A') + set(P(3,3)>0) + set(t+y > 7) + set(P(2,2)>4)+set(P(1,1:2)>t) + set(t>12)+set(t>-12); |
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| 106 | obj = trace(P)+y+t; |
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| 107 | fail = regresstest(F,obj,ops); |
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| 108 | regressreport('Test 10',fail) |
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| 109 | |
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| 110 | yalmip('clear') |
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| 111 | A = randn(3,3);A = -A*A'; |
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| 112 | P = sdpvar(3,3); |
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| 113 | t = sdpvar(1,1); |
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| 114 | y = sdpvar(1,1); |
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| 115 | F = set(A'*P+P*A < -eye(3)); |
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| 116 | F = F + set(P > A*A') + set(P(3,3)>0) + set(P>0) + set(t+y > 7) + set(P(2,2)>4)+set(P(1,1:2)>t) + set(t>12)+set(t>-12); |
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| 117 | obj = trace(P)+y+t; |
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| 118 | fail = regresstest(F,obj,ops); |
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| 119 | regressreport('Test 11',fail) |
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| 120 | |
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| 121 | %yalmip('clear') |
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| 122 | A = randn(3,3);A = -A*A'; |
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| 123 | P = sdpvar(3,3); |
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| 124 | %t = sdpvar(1,1); |
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| 125 | y = sdpvar(1,1); |
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| 126 | F = set(A'*P+P*A < -eye(3)); |
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| 127 | F = F + set(P > A*A') + set(P(3,3)>0) + set(P>0) + set(t+y > 7) + set(t+y > 7) + set(P(2,2)>4)+set(P(1,1:2)>t) + set(t>12)+set(t>-12); |
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| 128 | obj = trace(P)+y+t; |
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| 129 | fail = regresstest(F,obj,ops); |
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| 130 | regressreport('Test 12',fail) |
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| 131 | |
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| 132 | yalmip('clear') |
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| 133 | A = randn(3,3);A = -A*A'; |
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| 134 | P = sdpvar(3,3); |
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| 135 | t = sdpvar(1,1); |
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| 136 | y = sdpvar(1,1); |
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| 137 | F = set(A'*P+P*A < -eye(3)); |
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| 138 | F = F + set(2*P > A*A') + set(P(3,3)>0) + set(P>0) + set(t+y > 7) + set(t+y > 7) + set(P(2,2)>4)+set(P(1,1:2)>t) + set(t>12)+set(t>-12); |
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| 139 | obj = trace(P)+y+t; |
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| 140 | fail = regresstest(F,obj,ops); |
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| 141 | regressreport('Test 13',fail) |
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| 142 | |
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| 143 | |
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| 144 | |
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| 145 | |
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| 146 | function regressreport(text,fail) |
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| 147 | |
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| 148 | switch fail |
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| 149 | case 0 |
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| 150 | disp(['No problems in ' text]); |
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| 151 | case 1 |
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| 152 | disp(['Objective differ in ' text]); |
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| 153 | case 2 |
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| 154 | disp(['Infeasible solution in ' text]); |
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| 155 | otherwise |
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| 156 | end |
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| 157 | |
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| 158 | |
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| 159 | function fail = regresstest(F,obj,ops); |
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| 160 | solvesdp(F,obj,ops); |
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| 161 | obj1 = double(obj); |
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| 162 | p1 = checkset(F); |
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| 163 | |
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| 164 | x = recover(getvariables(F)); |
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| 165 | setsdpvar(x,0*double(x)); |
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| 166 | |
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| 167 | [Fdual,objdual,X,free,err] = dualize(F,obj); |
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| 168 | solvesdp(Fdual,-objdual,ops); |
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| 169 | |
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| 170 | if length(X)>0 |
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| 171 | for i = 1:length(X);setsdpvar(X{i},dual(Fdual(i)));end |
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| 172 | end |
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| 173 | if ~isempty(free) |
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| 174 | setsdpvar(free,dual(Fdual(end))); |
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| 175 | end |
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| 176 | |
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| 177 | obj2 = double(obj); |
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| 178 | p2 = checkset(Fdual); |
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| 179 | |
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| 180 | fail = 0; |
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| 181 | |
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| 182 | if abs(obj1-obj2) > 1e-4 |
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| 183 | fail = 1; |
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| 184 | [obj1 obj2] |
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| 185 | end |
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| 186 | if any(p2<-1e-5) |
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| 187 | fail = 2; |
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| 188 | end |
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| 189 | |
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