Example description

 E04RYF Example Program Results

 Freshly created handle
 Overview
   Status:                  Problem and option settings are editable.
   No of variables:         2
   Objective function:      not defined yet
   Simple bounds:           not defined yet
   Linear constraints:      not defined yet
   Nonlinear constraints:   not defined yet
   Matrix constraints:      not defined yet

 Handle after definition of simple bounds and the objective
 Overview
   Status:                  Problem and option settings are editable.
   No of variables:         2
   Objective function:      linear
   Simple bounds:           defined
   Linear constraints:      not defined yet
   Nonlinear constraints:   not defined yet
   Matrix constraints:      not defined yet
 Objective function
   linear part
   c(      2) =  1.00E+00,
 Simple bounds
    0.000E+00 <= X_      1
   -3.000E+00 <= X_      2 <=  3.000E+00

 Handle after definition of the 1st matrix constraint
 Overview
   Status:                  Problem and option settings are editable.
   No of variables:         2
   Objective function:      linear
   Simple bounds:           defined
   Linear constraints:      not defined yet
   Nonlinear constraints:   not defined yet
   Matrix constraints:      1
 Matrix constraints
   IDblk =     1, size =      3 x     3, linear

 Handle after partial definition of the 2nd matrix constraint
 Matrix constraints
   IDblk =     1, size =      3 x     3, linear
   IDblk =     2, size =      2 x     2, linear

 Handle with the complete problem formulation
 Overview
   Status:                  Problem and option settings are editable.
   No of variables:         2
   Objective function:      linear
   Simple bounds:           defined
   Linear constraints:      not defined yet
   Nonlinear constraints:   not defined yet
   Matrix constraints:      2
 Matrix constraints
   IDblk =     1, size =      3 x     3, linear
   IDblk =     2, size =      2 x     2, polynomial of order 2
 Lagrangian multipliers sizes
   (Standard) multipliers U: 4 + 0 + 0
   Matrix multipliers UA:    9
 Matrix constraints (detailed)
   Matrix inequality IDBLK =     1, dimension     3
     multiindex k =     0
       A_k(     1,     1) = -1.000E+00
       A_k(     2,     1) =  1.000E+00
       A_k(     2,     2) = -7.500E-01
       A_k(     3,     3) = -1.600E+01
 
     multiindex k =     1
       A_k(     2,     1) =  1.000E+00
 
     multiindex k =     2
       A_k(     3,     1) =  1.000E+00
 
   Matrix inequality IDBLK =     2, dimension     2
     multiindex k =     0
       A_k(     2,     2) = -1.000E+00
 
     multiindex k =     1
       A_k(     1,     1) =  1.000E+00
 
     multiindex k =     1,     2
       Q_k(     2,     1) = -1.000E+00
 

 Option settings
 Begin of Options
     Outer Iteration Limit         =                 100     * d
     Inner Iteration Limit         =                 100     * d
     Infinite Bound Size           =         1.00000E+20     * d
     Initial X                     =           Automatic     * U
     Initial U                     =           Automatic     * d
     Initial P                     =           Automatic     * d
     Hessian Density               =                Auto     * d
     Init Value P                  =         1.00000E+00     * d
     Init Value Pmat               =         1.00000E+00     * d
     Presolve Block Detect         =                 Yes     * d
     Print File                    =                   6     * d
     Print Level                   =                   2     * d
     Print Options                 =                  No     * U
     Print Solution                =                  No     * d
     Monitoring File               =                  -1     * d
     Monitoring Level              =                   4     * d
     Monitor Frequency             =                   0     * d
     Stats Time                    =                  No     * d
     P Min                         =         1.05367E-08     * d
     Pmat Min                      =         1.05367E-08     * d
     U Update Restriction          =         5.00000E-01     * d
     Umat Update Restriction       =         3.00000E-01     * d
     Preference                    =               Speed     * d
     Transform Constraints         =                Auto     * d
     Dimacs Measures               =               Check     * 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
     Linesearch Mode               =                Auto     * d
     Inner Stop Tolerance          =         1.00000E-02     * d
     Inner Stop Criteria           =           Heuristic     * d
     Task                          =            Minimize     * d
     P Update Speed                =                  12     * d
     Hessian Mode                  =                Auto     * d
     Verify Derivatives            =                  No     * d
     Time Limit                    =         1.00000E+06     * d
     Lpipm Centrality Correctors   =                   6     * d
     Lp Presolve                   =                 Yes     * d
     Lpipm Scaling                 =          Arithmetic     * d
     Lpipm System Formulation      =                Auto     * d
     Lpipm Algorithm               =         Primal-dual     * d
     Lpipm Stop Tolerance          =         1.05367E-08     * d
     Lpipm Monitor Frequency       =                   0     * d
     Lpipm Stop Tolerance 2        =         2.67452E-10     * d
     Lpipm Max Iterative Refinement=                   5     * d
     Lpipm Iteration Limit         =                 100     * d
     Dfls Trust Region Tolerance   =         1.24969E-06     * d
     Dfls Max Objective Calls      =                 500     * d
     Dfls Starting Trust Region    =         1.00000E-01     * d
     Dfls Number Interp Points     =                   0     * d
     Dfls Monitor Frequency        =                   0     * d
     Dfls Print Frequency          =                   1     * d
     Dfls Small Residuals Tol      =         1.08158E-12     * d
     Dfls Maximum Slow Steps       =                  20     * d
     Dfls Trust Region Slow Tol    =         1.02648E-04     * d
     Matrix Ordering               =                Auto     * d
     Dfls Number Initial Points    =                   0     * d
     Dfls Number Soft Restarts Pts =                   3     * d
     Dfls Max Soft Restarts        =                   5     * d
     Dfls Max Unsucc Soft Restarts =                   3     * d
     Dfls Noise Level              =         0.00000E+00     * d
     Dfls Random Seed              =                  -1     * d
 End of Options
 E04SV, NLP-SDP Solver (Pennon)
 ------------------------------
 Number of variables             2                 [eliminated            0]
                            simple  linear  nonlin
 (Standard) inequalities         3       0       0
 (Standard) equalities                   0       0
 Matrix inequalities                     1       1 [dense    2, sparse    0]
                                                   [max dimension         3]
 
 --------------------------------------------------------------
  it|  objective |  optim  |   feas  |  compl  | pen min |inner
 --------------------------------------------------------------
   0  0.00000E+00  4.56E+00  1.23E-01  4.41E+01  1.00E+00   0
   1 -3.01854E-01  1.21E-03  0.00E+00  1.89E+00  1.00E+00   7
   2 -6.21230E-01  2.58E-03  0.00E+00  6.72E-01  4.65E-01   2
   3 -2.11706E+00  4.31E-03  3.39E-02  6.07E-02  2.16E-01   5
   4 -2.01852E+00  5.71E-03  6.05E-03  8.55E-03  1.01E-01   3
   5 -2.00164E+00  3.36E-03  6.26E-04  1.02E-03  4.68E-02   2
   6 -2.00022E+00  4.45E-03  8.37E-05  1.82E-04  2.18E-02   1
   7 -2.00001E+00  4.73E-04  4.01E-06  3.96E-05  1.01E-02   1
   8 -2.00000E+00  4.77E-06  2.25E-07  9.20E-06  4.71E-03   1
   9 -2.00000E+00  4.52E-08  3.61E-08  2.14E-06  2.19E-03   1
  10 -2.00000E+00  6.63E-09  3.19E-08  4.98E-07  1.02E-03   1
  11 -2.00000E+00  8.80E-10  5.34E-09  1.16E-07  4.74E-04   1
  12 -2.00000E+00  1.02E-10  5.41E-09  2.69E-08  2.21E-04   1
 --------------------------------------------------------------
 Status: converged, an optimal solution found
 --------------------------------------------------------------
 Final objective value               -2.000000E+00
 Relative precision                   9.839057E-10
 Optimality                           1.019125E-10
 Feasibility                          5.406175E-09
 Complementarity                      2.693704E-08
 Iteration counts
   Outer iterations                             12
   Inner iterations                             26
   Linesearch steps                             37
 Evaluation counts
   Augm. Lagr. values                           50
   Augm. Lagr. gradient                         39
   Augm. Lagr. hessian                          26
 --------------------------------------------------------------

 Problem solved
 Overview
   Status:                  Solver finished, only options can be changed.
   No of variables:         2
   Objective function:      linear
   Simple bounds:           defined
   Linear constraints:      not defined
   Nonlinear constraints:   not defined
   Matrix constraints:      2

 Final objective value =     -2.00
 Final X =      0.25    -2.00