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<title>Builds and solves a simple inequality-constrained linear program</title>
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<h1>Builds and solves a simple inequality-constrained linear program</h1>
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<pre class="codeinput">
echo <span class="string">on</span>
n = 10;
A = randn(2*n,n);
b = randn(2*n,1);
c = randn(n,1);
d = randn;
cvx_begin
variable <span class="string">x(n)</span>
dual <span class="string">variables</span> <span class="string">y</span> <span class="string">z</span>
minimize( c' * x + d )
subject <span class="string">to</span>
y : A * x &lt;= b;
cvx_end
echo <span class="string">off</span>
</pre>
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<pre class="codeoutput">
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 &lt;= b;
cvx_end
Calling SDPT3: 20 variables, 10 equality constraints
For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------
num. of constraints = 10
dim. of linear var = 20
*******************************************************************
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|3.2e+01|8.5e+00|2.0e+03| 3.617354e+01 0.000000e+00| 0:0:00| chol 1 1
1|0.653|0.803|1.1e+01|1.7e+00|7.4e+02| 4.479851e+01 -1.562618e+01| 0:0:00| chol 1 1
2|0.998|0.766|2.5e-02|4.1e-01|1.6e+02| 7.884226e+01 -1.557992e+01| 0:0:00| chol 1 1
3|1.000|1.000|3.0e-05|8.6e-04|1.7e+01| 1.198552e+01 -5.409116e+00| 0:0:00| chol 1 1
4|1.000|1.000|1.1e-06|9.2e-05|5.6e+00| 5.721277e+00 1.093864e-01| 0:0:00| chol 1 1
5|1.000|0.694|7.5e-08|3.4e-05|3.6e+00| 5.868670e+00 2.239060e+00| 0:0:00| chol 1 1
6|1.000|1.000|6.9e-09|8.8e-07|9.8e-01| 3.886363e+00 2.903232e+00| 0:0:00| chol 1 1
7|0.811|0.963|2.7e-09|1.2e-07|2.4e-01| 3.448018e+00 3.207296e+00| 0:0:00| chol 1 1
8|1.000|1.000|1.4e-09|9.2e-09|5.3e-02| 3.335759e+00 3.282517e+00| 0:0:00| chol 1 1
9|0.975|0.985|3.4e-10|1.3e-09|1.1e-03| 3.307185e+00 3.306084e+00| 0:0:00| chol 1 1
10|0.989|0.989|3.9e-12|1.7e-10|1.3e-05| 3.306547e+00 3.306534e+00| 0:0:00| chol 1 1
11|0.996|0.996|5.2e-14|1.6e-12|1.9e-07| 3.306540e+00 3.306539e+00| 0:0:00| chol 1 1
12|0.998|0.998|2.6e-14|1.0e-12|2.3e-09| 3.306539e+00 3.306539e+00| 0:0:00|
stop: max(relative gap, infeasibilities) &lt; 1.49e-08
-------------------------------------------------------------------
number of iterations = 12
primal objective value = 3.30653941e+00
dual objective value = 3.30653941e+00
gap := trace(XZ) = 2.30e-09
relative gap = 3.03e-10
actual relative gap = 3.01e-10
rel. primal infeas = 2.61e-14
rel. dual infeas = 1.00e-12
norm(X), norm(y), norm(Z) = 3.9e+00, 2.3e+00, 9.1e+00
norm(A), norm(b), norm(C) = 1.6e+01, 4.6e+00, 5.2e+00
Total CPU time (secs) = 0.11
CPU time per iteration = 0.01
termination code = 0
DIMACS: 4.0e-14 0.0e+00 1.5e-12 0.0e+00 3.0e-10 3.0e-10
-------------------------------------------------------------------
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -5.32653
echo off
</pre>
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