Example description

 E04SVF Example Program Results

 E04SV, NLP-SDP Solver (Pennon)
 ------------------------------
 Number of variables            16                 [eliminated            0]
                            simple  linear  nonlin
 (Standard) inequalities         0       0       0
 (Standard) equalities                   0       0
 Matrix inequalities                     1       0 [dense    1, sparse    0]
                                                   [max dimension        10]
 
 Begin of Options
     Print File                    =                   6     * d
     Print Level                   =                   2     * d
     Print Options                 =                 Yes     * d
     Monitoring File               =                  -1     * d
     Monitoring Level              =                   4     * d
     Monitor Frequency             =                   0     * d
 
     Infinite Bound Size           =         1.00000E+20     * d
     Task                          =            Minimize     * d
     Stats Time                    =                  No     * d
 
     Dimacs Measures               =               Check     * d
     Hessian Density               =               Dense     * S
     Init Value P                  =         1.00000E+00     * d
     Init Value Pmat               =         1.00000E+00     * d
     Initial P                     =           Automatic     * d
     Initial U                     =           Automatic     * d
     Initial X                     =           Automatic     * U
     Inner Iteration Limit         =                 100     * d
     Inner Stop Criteria           =           Heuristic     * d
     Inner Stop Tolerance          =         1.00000E-02     * d
     Linesearch Mode               =            Fullstep     * S
     Outer Iteration Limit         =                 100     * d
     P Min                         =         1.05367E-08     * d
     P Update Speed                =                  12     * d
     Pmat Min                      =         1.05367E-08     * d
     Preference                    =               Speed     * d
     Presolve Block Detect         =                 Yes     * d
     Stop Criteria                 =                Soft     * d
     Stop Tolerance 1              =         1.00000E-06     * d
     Stop Tolerance 2              =         1.00000E-07     * d
     Stop Tolerance Feasibility    =         1.00000E-07     * d
     Transform Constraints         =                  No     * S
     U Update Restriction          =         5.00000E-01     * d
     Umat Update Restriction       =         3.00000E-01     * d
 End of Options
 --------------------------------------------------------------
  it|  objective |  optim  |   feas  |  compl  | pen min |inner
 --------------------------------------------------------------
   0  0.00000E+00  4.71E+01  1.00E+01  4.81E+01  1.60E+01   0
   1  9.55399E+01  9.29E-03  0.00E+00  9.52E+01  1.60E+01   8
   2  3.93849E+01  1.16E-03  0.00E+00  3.81E+01  6.63E+00   5
   3  1.68392E+01  1.19E-02  0.00E+00  1.52E+01  2.75E+00   3
   4  8.50544E+00  7.32E-04  0.00E+00  5.78E+00  1.14E+00   4
   5  5.62254E+00  1.56E-02  0.00E+00  2.07E+00  4.72E-01   3
   6  4.63348E+00  7.66E-03  0.00E+00  7.33E-01  1.96E-01   4
   7  4.25322E+00  2.99E-03  0.00E+00  2.72E-01  8.11E-02   4
   8  4.10154E+00  2.41E-03  0.00E+00  1.05E-01  3.36E-02   4
   9  4.04076E+00  1.87E-03  0.00E+00  4.14E-02  1.39E-02   4
  10  4.01631E+00  6.25E-03  0.00E+00  1.65E-02  5.77E-03   5
  11  4.00656E+00  3.23E-03  0.00E+00  6.59E-03  2.39E-03   5
  12  4.00263E+00  2.89E-03  0.00E+00  2.64E-03  9.91E-04   5
  13  4.00106E+00  2.08E-03  0.00E+00  1.06E-03  4.11E-04   5
  14  4.00042E+00  1.53E-03  0.00E+00  4.25E-04  1.70E-04   5
 --------------------------------------------------------------
  it|  objective |  optim  |   feas  |  compl  | pen min |inner
 --------------------------------------------------------------
  15  4.00017E+00  1.30E-06  0.00E+00  1.70E-04  7.05E-05   6
  16  4.00007E+00  7.48E-07  0.00E+00  6.82E-05  2.92E-05   6
  17  4.00003E+00  3.20E-07  0.00E+00  2.73E-05  1.21E-05   6
  18  4.00001E+00  1.31E-07  0.00E+00  1.10E-05  5.02E-06   6
  19  4.00000E+00  5.15E-08  0.00E+00  4.39E-06  2.08E-06   6
  20  4.00000E+00  1.92E-08  0.00E+00  1.76E-06  8.62E-07   6
  21  4.00000E+00  7.13E-09  0.00E+00  7.05E-07  3.57E-07   6
  22  4.00000E+00  2.09E-09  0.00E+00  2.82E-07  1.48E-07   6
 --------------------------------------------------------------
 Status: converged, an optimal solution found
 --------------------------------------------------------------
 Final objective value                4.000000E+00
 Relative precision                   8.450361E-08
 Optimality                           2.088293E-09
 Feasibility                          0.000000E+00
 Complementarity                      2.822749E-07
 DIMACS error 1                       1.044147E-09
 DIMACS error 2                       0.000000E+00
 DIMACS error 3                       0.000000E+00
 DIMACS error 4                       0.000000E+00
 DIMACS error 5                       3.294796E-08
 DIMACS error 6                       3.136387E-08
 Iteration counts
   Outer iterations                             22
   Inner iterations                            112
   Linesearch steps                            308
 Evaluation counts
   Augm. Lagr. values                          135
   Augm. Lagr. gradient                        135
   Augm. Lagr. hessian                         112
 --------------------------------------------------------------
 The solver chose to use DENSE hessian
 and FULLSTEP as linesearch.
 Lovasz theta number of the given graph is    4.00