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.
------------------------------------------------------------

 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      mean(obj)   cputime
-------------------------------------------------------------------
 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
-------------------------------------------------------------------
 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
-------------------------------------------------------------------
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -0.188114