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<title>Builds and solves a simple least-squares problem using cvx</title>
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<h1>Builds and solves a simple least-squares problem using cvx</h1>
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<pre class="codeinput">
echo <span class="string">on</span>
n = 100;
A = randn(2*n,n);
b = randn(2*n,1);
cvx_begin
variable <span class="string">x(n)</span>
minimize( norm( A*x-b ) )
cvx_end
echo <span class="string">off</span>
</pre>
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<pre class="codeoutput">
n = 100;
A = randn(2*n,n);
b = randn(2*n,1);
cvx_begin
variable x(n)
minimize( norm( A*x-b ) )
cvx_end
Calling SDPT3: 201 variables, 101 equality constraints
For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------
num. of constraints = 101
dim. of socp var = 201, num. of socp blk = 1
*******************************************************************
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|6.6e+00|1.5e+00|2.5e+02| 0.000000e+00 0.000000e+00| 0:0:00| chol 1 1
1|0.957|1.000|2.9e-01|6.6e-03|2.3e+01|-9.691971e+00 -2.045281e+01| 0:0:00| chol 1 1
2|1.000|1.000|7.3e-08|6.6e-04|1.4e+00|-8.725326e+00 -1.014181e+01| 0:0:00| chol 1 1
3|0.985|0.986|1.8e-08|7.5e-05|2.1e-02|-9.515525e+00 -9.535125e+00| 0:0:00| chol 1 1
4|0.989|0.989|5.6e-09|7.4e-06|2.3e-04|-9.527047e+00 -9.527166e+00| 0:0:00| chol 1 1
5|0.989|0.989|6.2e-11|8.2e-08|2.5e-06|-9.527175e+00 -9.527176e+00| 0:0:00| chol 1 1
6|0.989|0.989|1.0e-12|9.1e-10|2.8e-08|-9.527176e+00 -9.527176e+00| 0:0:00|
stop: max(relative gap, infeasibilities) &lt; 1.49e-08
-------------------------------------------------------------------
number of iterations = 6
primal objective value = -9.52717641e+00
dual objective value = -9.52717642e+00
gap := trace(XZ) = 2.81e-08
relative gap = 1.40e-09
actual relative gap = 7.16e-10
rel. primal infeas = 1.00e-12
rel. dual infeas = 9.13e-10
norm(X), norm(y), norm(Z) = 1.4e+00, 9.6e+00, 1.3e+01
norm(A), norm(b), norm(C) = 1.4e+02, 2.0e+00, 1.5e+01
Total CPU time (secs) = 0.11
CPU time per iteration = 0.02
termination code = 0
DIMACS: 1.0e-12 0.0e+00 3.5e-09 0.0e+00 7.2e-10 1.4e-09
-------------------------------------------------------------------
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +9.52718
echo off
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