Builds and solves a simple inequality-constrained linear program
echo on
n = 10;
A = randn(2*n,n);
b = randn(2*n,1);
c = randn(n,1);
d = randn;
cvx_begin
variable x(n)
dual variables y z
minimize( c' * x + d )
subject to
y : A * x <= b;
cvx_end
echo off
Calling SDPT3: 20 variables, 10 equality constraints
For improved efficiency, SDPT3 is solving the dual problem.
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num. of constraints = 10
dim. of linear var = 20
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SDPT3: Infeasible path-following algorithms
*******************************************************************
version predcorr gam expon scale_data
NT 1 0.000 1 0
it pstep dstep pinfeas dinfeas gap mean(obj) cputime
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0|0.000|0.000|1.9e+01|4.4e+00|6.0e+02| 1.094136e+01| 0:0:00| chol 1 1
1|0.650|0.842|6.6e+00|7.5e-01|1.9e+02|-3.816421e+00| 0:0:00| chol 1 1
2|0.762|1.000|1.6e+00|6.7e-03|5.3e+01|-6.080676e+00| 0:0:00| chol 1 1
3|0.884|1.000|1.8e-01|6.7e-04|9.0e+00|-3.201150e+00| 0:0:00| chol 1 1
4|1.000|0.971|4.6e-07|8.5e-05|1.3e+00|-9.606439e-01| 0:0:00| chol 1 1
5|1.000|1.000|1.5e-08|6.8e-06|3.2e-01|-7.956066e-01| 0:0:00| chol 1 1
6|0.972|0.945|4.5e-09|1.0e-06|1.6e-02|-7.526928e-01| 0:0:00| chol 1 1
7|0.993|1.000|1.0e-09|6.8e-08|5.3e-03|-7.524633e-01| 0:0:00| chol 1 1
8|1.000|0.972|3.1e-10|8.6e-09|3.4e-04|-7.522972e-01| 0:0:00| chol 1 1
9|0.988|0.988|1.1e-10|8.3e-10|4.2e-06|-7.522721e-01| 0:0:00| chol 1 1
10|0.997|0.995|3.7e-13|2.6e-11|6.5e-08|-7.522719e-01| 0:0:00| chol 1 1
11|0.999|0.997|9.0e-15|1.1e-12|8.3e-10|-7.522719e-01| 0:0:00|
stop: max(relative gap, infeasibilities) < 1.49e-08
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number of iterations = 11
primal objective value = -7.52271851e-01
dual objective value = -7.52271852e-01
gap := trace(XZ) = 8.33e-10
relative gap = 3.33e-10
actual relative gap = 3.27e-10
rel. primal infeas = 8.98e-15
rel. dual infeas = 1.08e-12
norm(X), norm(y), norm(Z) = 3.6e+00, 3.3e+00, 1.5e+01
norm(A), norm(b), norm(C) = 1.5e+01, 3.8e+00, 6.7e+00
Total CPU time (secs) = 0.1
CPU time per iteration = 0.0
termination code = 0
DIMACS: 1.1e-14 0.0e+00 1.6e-12 0.0e+00 3.3e-10 3.3e-10
-------------------------------------------------------------------
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Status: Solved
Optimal value (cvx_optval): -0.188114