NAG Library Manual, Mark 28.7
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NAG FL Interface Introduction
Example description

 E04RDF Example Program Results

 Reading SDPA file: e04rdfe.opt
 ** At least one of maxnvar, maxnblk or maxnnz is too small.
 ** maxnvar should be at least                    2, was                    0.
 ** maxnblk should be at least                    3, was                    0.
 ** maxnnz should be at least                   10, was                    0.
 ** ABNORMAL EXIT from NAG Library routine e04rdf: IFAIL =     1
 ** NAG soft failure - control returned
 Allocating space for the problem.
      NVAR =       2
      NBLK =       3
      NNZ  =      10
 Linear SDP problem was read, start formulating the problem
 The problem formulation in a handle is completed.

 Overview
   Status:                  Problem and option settings are editable.
   No of variables:         2
   Objective function:      linear
   Simple bounds:           not defined yet
   Linear constraints:      not defined yet
   Nonlinear constraints:   not defined yet
   Cone constraints:        not defined yet
   Quadratic constraints:   not defined yet
   Matrix constraints:      3
 
 --------------------------------
  E04SV, NLP-SDP Solver (Pennon)
 --------------------------------
 
 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     * U
     Hessian Density               =                Auto     * d
     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               =                Auto     * d
     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         =                Auto     * d
     U Update Restriction          =         5.00000E-01     * d
     Umat Update Restriction       =         3.00000E-01     * d
 End of Options
 
 Problem Statistics
   No of variables                  2
     bounds               not defined
   No of lin. constraints           0
     nonzeroes                      0
   No of matrix inequal.            3
     detected matrix inq.           1
       linear                       1
       nonlinear                    0
       max. dimension               2
     detected normal inq.           2
       linear                       2
       nonlinear                    0
   Objective function          Linear
 
 Begin of options modified by the solver
     Hessian Density               =               Dense     * S
     Linesearch Mode               =            Fullstep     * S
     Transform Constraints         =                  No     * S
 End of Options
 
 --------------------------------------------------------------
  it|  objective |  optim  |   feas  |  compl  | pen min |inner
 --------------------------------------------------------------
   0  0.00000E+00  4.06E+01  4.00E+00  3.16E+01  1.00E+00   0
   1  4.02661E+01  1.07E-01  2.78E-01  1.52E+01  1.00E+00   5
   2  2.90783E+01  6.52E-02  9.77E-02  2.78E+00  4.65E-01   5
   3  2.84228E+01  1.67E-01  2.39E-01  7.76E-01  2.16E-01   2
   4  2.97263E+01  3.98E-02  4.39E-02  2.05E-01  1.01E-01   3
   5  2.99618E+01  5.01E-02  6.40E-03  3.32E-02  4.68E-02   2
   6  2.99934E+01  1.45E-01  1.25E-03  6.23E-03  2.18E-02   1
   7  2.99999E+01  3.31E-02  1.28E-05  4.16E-04  1.01E-02   1
   8  3.00001E+01  9.97E-05  3.01E-07  9.67E-05  4.71E-03   1
   9  3.00000E+01  1.37E-04  3.25E-08  2.25E-05  2.19E-03   1
  10  3.00000E+01  1.16E-05  3.52E-09  5.23E-06  1.02E-03   1
  11  3.00000E+01  1.13E-06  3.81E-10  1.22E-06  4.74E-04   1
 --------------------------------------------------------------
 Status: converged, an optimal solution found
 --------------------------------------------------------------
 Final objective value                3.000000E+01
 Relative precision                   3.941484E-08
 Optimality                           1.133096E-06
 Feasibility                          3.806810E-10
 Complementarity                      1.216064E-06
 DIMACS error 1                       5.395697E-08
 DIMACS error 2                       0.000000E+00
 DIMACS error 3                       0.000000E+00
 DIMACS error 4                       7.613621E-11
 DIMACS error 5                       4.324629E-09
 DIMACS error 6                       2.296238E-08
 Iteration counts
   Outer iterations                             11
   Inner iterations                             23
   Linesearch steps                             50
 Evaluation counts
   Augm. Lagr. values                           35
   Augm. Lagr. gradient                         35
   Augm. Lagr. hessian                          23
 --------------------------------------------------------------

 Optimal solution:
 X =      1.00     1.00
 Lagrangian multiplier for A_1
             1
 1     10.0000
 Lagrangian multiplier for A_2
               1
 1    2.4321E-06
 Lagrangian multiplier for A_3
             1          2
 1      2.8571
 2     -2.8571     2.8571