disp('Sept 29/09 ')
Sept 29/09 
startupcvx   % personal startup command to add correct paths
  addpath c:\software.d\cvx\builtins
    addpath c:\software.d\cvx\commands
    addpath c:\software.d\cvx\functions
    addpath c:\software.d\cvx\lib
    addpath c:\software.d\cvx\structures
    addpath c:\software.d\cvx\examples
    addpath c:\software.d\cvx
%More involved example
A = randn(5);
A = A'*A

A =

  Columns 1 through 4

   2.374791125997622  -1.261506979703491   1.199822624319685  -1.244322036356210
  -1.261506979703491   2.941377925419477  -2.456796665967557   0.364608040358330
   1.199822624319685  -2.456796665967557   2.811459885871691  -0.188344633127809
  -1.244322036356210   0.364608040358330  -0.188344633127809   1.073515279235954
  -0.599007839626273   1.326417206570953  -2.289815591498254  -0.321197779649739

  Column 5

  -0.599007839626273
   1.326417206570953
  -2.289815591498254
  -0.321197779649739
   2.582039539640861

cvx_begin
variable X(5, 5) symmetric;
variable y;
minimize(norm(X) - 10*sqrt(y))
subject to
X - A == semidefinite(5);
X(2,5) == 2*y;
X(3,1) >= 0.8;
y <= 4;
cvx_end
 
Calling SDPT3: 75 variables, 17 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 17
 dim. of sdp    var  = 17,   num. of sdp  blk  =  3
 dim. of linear var  =  2
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      mean(obj)   cputime
-------------------------------------------------------------------
 0|0.000|0.000|1.0e+002|3.0e+000|7.3e+003|-2.945910e+002| 0:0:00| chol  1  1 
 1|0.604|0.726|4.0e+001|8.4e-001|2.7e+003|-4.925034e+002| 0:0:00| chol  1  1 
 2|0.708|1.000|1.2e+001|4.3e-003|1.4e+003|-9.571220e+001| 0:0:00| chol  1  1 
 3|0.887|1.000|1.3e+000|4.3e-004|1.6e+002|-1.468771e+001| 0:0:00| chol  1  1 
 4|0.540|0.711|6.0e-001|1.5e-004|1.1e+002| 3.125571e+000| 0:0:00| chol  1  1 
 5|0.864|1.000|8.2e-002|4.3e-006|1.9e+001| 4.741185e+000| 0:0:00| chol  1  1 
 6|0.935|1.000|5.3e-003|1.6e-002|5.7e+000| 5.149158e+000| 0:0:00| chol  1  1 
 7|0.988|1.000|6.3e-005|1.1e-003|1.1e+000| 4.967965e+000| 0:0:00| chol  1  1 
 8|1.000|1.000|1.1e-009|1.3e-005|2.9e-001| 4.893424e+000| 0:0:00| chol  1  1 
 9|0.925|0.972|5.9e-010|3.6e-007|3.3e-002| 4.822408e+000| 0:0:00| chol  1  1 
10|1.000|1.000|1.4e-012|1.6e-010|1.2e-002| 4.815123e+000| 0:0:00| chol  1  1 
11|0.953|0.938|4.5e-013|1.5e-011|1.1e-003| 4.811825e+000| 0:0:00| chol  1  1 
12|1.000|1.000|4.0e-012|1.4e-012|1.2e-004| 4.811476e+000| 0:0:00| chol  1  1 
13|0.988|0.988|7.1e-011|1.0e-012|1.5e-006| 4.811435e+000| 0:0:00| chol  1  2 
14|0.998|1.000|1.0e-010|1.5e-012|2.4e-008| 4.811434e+000| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.49e-008
-------------------------------------------------------------------
 number of iterations   = 14
 primal objective value =  4.81143413e+000
 dual   objective value =  4.81143411e+000
 gap := trace(XZ)       = 2.37e-008
 relative gap           = 2.24e-009
 actual relative gap    = 1.71e-009
 rel. primal infeas     = 1.01e-010
 rel. dual   infeas     = 1.50e-012
 norm(X), norm(y), norm(Z) = 1.0e+001, 1.4e+001, 3.1e+001
 norm(A), norm(b), norm(C) = 1.0e+001, 1.1e+001, 1.0e+001
 Total CPU time (secs)  = 0.4  
 CPU time per iteration = 0.0  
 termination code       =  0
 DIMACS: 1.0e-010  0.0e+000  3.1e-012  0.0e+000  1.7e-009  2.2e-009
-------------------------------------------------------------------
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): -4.81143
%Disciplined Convex Programming and CVX 18
format long
disp('optima')
optima
y

y =

   1.564563042126623

X

X =

  Columns 1 through 4

   4.373981408050321  -0.341962160803890   1.781099702030079  -0.576355228810058
  -0.341962160803890   4.679609107567827  -0.124440298095597   0.337158717138440
   1.781099702030079  -0.124440298095597   6.476908180158437  -0.036266842147615
  -0.576355228810058   0.337158717138440  -0.036266842147615   4.792935673023767
   0.354646545813196   3.129126084253246   0.129056956622673  -0.349665336837799

  Column 5

   0.354646545813196
   3.129126084253246
   0.129056956622673
  -0.349665336837799
   4.451617841486734

disp('constraints')
constraints
eig(X-A)

ans =

   0.000000001125806
   0.071975534203023
   1.684941304075837
   3.880296748532569
   7.354654866184248

X(2,5)-2*y

ans =

     0

X(3,1)-0.8

ans =

   0.981099702030079

echo off