Hi, I have use the folling code, but the result is negative? why? I used CVX 2.0, matlab R2010b
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
dd = [1 1 1 1 1 1 1 1 1 1 1];
cvx_begin
variable y(11)
minimize( norm(y - old_avg_pi , 2 ))
subject to
dd * y == 1
-y <= 0
cvx_end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
old_avg_pi =
1.0e+006 *
0.7696
1.3818
0.6645
5.8412
0.0000
0.4283
0.6691
3.9130
0.7088
1.4975
1.1092
Calling SDPT3 4.0: 23 variables, 12 equality constraints
num. of constraints = 12
dim. of socp var = 12, num. of socp blk = 1
dim. of linear var = 11
SDPT3: Infeasible path-following algorithms
version predcorr gam expon scale_data
NT 1 0.000 1 0
it pstep dstep pinfeas dinfeas gap prim-obj dual-obj cputime
0|0.000|0.000|9.8e+000|1.7e+001|6.3e+009| 1.362889e+007 0.000000e+000| 0:0:00| chol 1 1
1|0.972|0.968|2.7e-001|1.0e+000|1.8e+008| 9.062942e+006 9.803218e+006| 0:0:00| chol 1 1
2|0.983|1.000|4.7e-003|2.5e-001|3.1e+006| 7.640643e+006 8.613915e+006| 0:0:00| chol 1 1
3|0.989|0.993|5.3e-005|1.3e-001|3.5e+004| 7.549734e+006 8.096859e+006| 0:0:00| chol 2 2
4|0.942|1.000|3.1e-006|6.2e-002|2.0e+003| 7.548582e+006 7.820884e+006| 0:0:00| chol 2 2
5|0.899|1.000|3.1e-007|3.1e-002|2.6e+002| 7.548596e+006 7.684752e+006| 0:0:00| chol 3 3
6|0.961|1.000|1.2e-008|6.2e-008|1.9e+001| 7.548579e+006 7.548568e+006| 0:0:00| chol 11 7
7|1.000|1.000|4.0e-008|2.4e-009|1.8e+000| 7.548578e+006 7.548577e+006| 0:0:00| chol 20 30
8|1.000|0.524|1.5e-005|4.7e-009|8.6e-001| 7.548694e+006 7.548578e+006| 0:0:00| chol 15 8
9|0.617|1.000|5.9e-006|5.4e-009|4.1e-001| 7.548622e+006 7.548578e+006| 0:0:00| chol 7 10
10|0.998|0.848|7.6e-009|1.3e-009|2.5e-002| 7.548578e+006 7.548578e+006| 0:0:00|
stop: max(relative gap, infeasibilities) < 1.49e-008
number of iterations = 10
primal objective value = 7.54857799e+006
dual objective value = 7.54857813e+006
gap := trace(XZ) = 2.46e-002
relative gap = 1.63e-009
actual relative gap = -8.70e-009
rel. primal infeas = 7.62e-009
rel. dual infeas = 1.33e-009
norm(X), norm(y), norm(Z) = 1.1e+007, 2.2e+000, 2.5e+000
norm(A), norm(b), norm© = 6.7e+000, 1.9e+007, 2.0e+000
Total CPU time (secs) = 0.13
CPU time per iteration = 0.01
termination code = 0
DIMACS: 8.3e-009 0.0e+000 1.3e-009 0.0e+000 -8.7e-009 1.6e-009
Status: Solved
Optimal value (cvx_optval): +7.54858e+006
y =
0.0011
-0.0212
0.0046
1.1923
0.0016
0.0012
0.0094
-0.0084
-0.0285
0.0071
-0.0279