NAG Library Manual, Mark 29.3
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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
Cone 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
Cone 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
Cone 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
Cone 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 + 0
Cone multipliers UC:      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
Print File                    =                   6     * d
Print Level                   =                   2     * d
Print Options                 =                  No     * U
Print Solution                =                  No     * d
Monitoring File               =                  -1     * d
Monitoring Level              =                   4     * d
Dfo Print Frequency           =                   1     * d
Dfo Monitor Frequency         =                   0     * d
Foas Monitor Frequency        =                   0     * d
Foas Print Frequency          =                   1     * d
Lpipm Monitor Frequency       =                   0     * d
Monitor Frequency             =                   0     * d
Socp Monitor Frequency        =                   0     * d

Infinite Bound Size           =         1.00000E+20     * d
Stats Time                    =                  No     * d
Time Limit                    =         1.00000E+06     * d
Verify Derivatives            =                  No     * d
Reg Term Type                 =                 Off     * d
Reg Coefficient               =         1.00000E+00     * d

Dimacs Measures               =               Check     * d
Hessian Density               =                Auto     * d
Hessian Mode                  =                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
Matrix Ordering               =                Auto     * d
Matrix Ordering               =                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

Lp Presolve                   =                 Yes     * d
Lpipm Algorithm               =         Primal-dual     * d
Lpipm Centrality Correctors   =                   6     * d
Lpipm Iteration Limit         =                 100     * d
Lpipm Max Iterative Refinement=                   5     * d
Lpipm Scaling                 =          Arithmetic     * d
Lpipm Stop Tolerance          =         1.05367E-08     * d
Lpipm Stop Tolerance 2        =         2.67452E-10     * d
Lpipm System Formulation      =                Auto     * d

Dfo Initial Interp Points     =          Coordinate     * d
Dfo Max Objective Calls       =                 500     * d
Dfo Max Soft Restarts         =                   5     * d
Dfo Max Unsucc Soft Restarts  =                   3     * d
Dfo Maximum Slow Steps        =                  20     * d
Dfo Noise Level               =         0.00000E+00     * d
Dfo Noisy Problem             =                  No     * d
Dfo Number Initial Points     =                   0     * d
Dfo Number Interp Points      =                   0     * d
Dfo Number Soft Restarts Pts  =                   3     * d
Dfo Random Seed               =                  -1     * d
Dfo Starting Trust Region     =         1.00000E-01     * d
Dfo Trust Region Slow Tol     =         1.02648E-04     * d
Dfo Trust Region Tolerance    =         1.24969E-06     * d
Dfo Version                   =              Latest     * d
Dfls Small Residuals Tol      =         1.08158E-12     * d
Dfno Detect Unbounded         =                 Yes     * d
Dfno Objective Limit          =        -1.7977E+308     * d

Foas Estimate Derivatives     =                  No     * d
Foas Finite Diff Interval     =         1.05367E-08     * d
Foas Iteration Limit          =            10000000     * d
Foas Memory                   =                  11     * d
Foas Progress Tolerance       =         1.08158E-12     * d
Foas Rel Stop Tolerance       =         1.08158E-12     * d
Foas Restart Factor           =         6.00000E+00     * d
Foas Slow Tolerance           =         1.01316E-02     * d
Foas Stop Tolerance           =         1.00000E-06     * d
Foas Tolerance Norm           =            Infinity     * d

Socp Iteration Limit          =                 100     * d
Socp Max Iterative Refinement =                   9     * d
Socp Presolve                 =                 Yes     * d
Socp Scaling                  =                None     * d
Socp Stop Tolerance           =         1.05367E-08     * d
Socp Stop Tolerance 2         =         1.05367E-08     * d
Socp System Formulation       =    Augmented System     * d
Socp Factorization Method     =                Ma86     * d

Bxnl Model                    =              Hybrid     * d
Bxnl Nlls Method              =             Galahad     * d
Bxnl Glob Method              =                  Tr     * d
Bxnl Reg Order                =                Auto     * d
Bxnl Tn Method                =           Min-1-var     * d
Bxnl Basereg Type             =                None     * d
Bxnl Basereg Pow              =         2.00000E+00     * d
Bxnl Basereg Term             =         1.00000E-02     * d
Bxnl Iteration Limit          =                1000     * d
Bxnl Monitor Frequency        =                   0     * d
Bxnl Print Header             =                  30     * d
Bxnl Save Covariance Matrix   =                  No     * d
Bxnl Stop Abs Tol Fun         =         1.05367E-08     * d
Bxnl Stop Abs Tol Grd         =         1.05737E-05     * d
Bxnl Stop Rel Tol Fun         =         1.05367E-08     * d
Bxnl Stop Rel Tol Grd         =         1.05367E-08     * d
Bxnl Stop Step Tol            =         2.22045E-16     * d
Bxnl Use Second Derivatives   =                  No     * d
Bxnl Use Weights              =                  No     * d

Mcs Initialization Method     =       Simple Bounds     * d
Mcs Local Searches            =                  On     * d
Mcs Local Searches Limit      =                  50     * d
Mcs Local Searches Tolerance  =         2.22045E-16     * d
Mcs Max Objective Calls       =                   0     * d
Mcs Monitor Frequency         =                   0     * d
Mcs Repeatability             =                 Off     * d
Mcs Splits Limit              =                   0     * d
Mcs Static Limit              =                   0     * d
Mcs Target Objective Error    =         1.02648E-04     * d
Mcs Target Objective Safeguard=         1.05367E-08     * d
Mcs Target Objective Value    =        -1.7977E+308     * d
Mcs Print Frequency           =                   1     * d

Ssqp Crash Option             =         Triple-pass     * d
Ssqp Crash Tolerance          =         1.00000E-01     * d
Ssqp Estimate Derivatives     =                  No     * d
Ssqp Finite Diff Ctrl Interval=         6.69433E-05     * d
Ssqp Finite Diff Interval     =         5.47723E-07     * d
Ssqp Function Precision       =         3.00000E-13     * d
Ssqp Hessian                  =                Auto     * d
Ssqp Hessian Updates          =                  10     * d
Ssqp Iteration Limit          =               10000     * d
Ssqp Major Feasibility Tol    =         1.00001E-06     * d
Ssqp Major Iteration Limit    =                1000     * d
Ssqp Major Optimality Tol     =         1.00001E-06     * d
Ssqp Minor Feasibility Tol    =         1.00001E-06     * d
Ssqp Minor Iteration Limit    =                 500     * d
Ssqp Monitor Frequency        =                   0     * d
Ssqp Penalty Parameter        =         0.00000E+00     * d
Ssqp Print Frequency          =                   1     * d
Ssqp Scale Option             =                None     * d
Ssqp Scale Print              =                  No     * d
Ssqp Scale Tolerance          =         9.00000E-01     * d
Ssqp Start Type               =                Cold     * d
Ssqp Superbasics Limit        =                  -1     * d

Nldf Loss Function Type       =                  L2     * d
Nldf Huber Function Width     =         1.00000E+00     * d
Nldf Cauchy Function Sharpness=         1.00000E+00     * d
Nldf Smoothl1 Function Width  =         1.00000E+00     * d
Nldf Quantile Parameter       =         5.00000E-01     * d
Nldf Iteration Limit          =            10000000     * d
Nldf Stop Tolerance           =         1.00000E-06     * d
Nldf Monitor Frequency        =                   0     * d

Milp Presolve                 =                 Yes     * d
Milp Random Seed              =                   0     * d
Milp Feasibility Tol          =         1.00000E-06     * d
Milp Rel Gap                  =         1.00000E-04     * d
Milp Abs Gap                  =         1.00000E-06     * d
Milp Small Matrix Value       =         1.00000E-09     * d
Milp Detect Symmetry          =                 Yes     * d
Milp Max Nodes                =          2147483647     * d
End of Options

--------------------------------
E04SV, NLP-SDP Solver (Pennon)
--------------------------------

Problem Statistics
No of variables                  2
free (unconstrained)           0
bounded                        2
No of lin. constraints           0
nonzeroes                      0
No of matrix inequal.            2
detected matrix inq.           2
linear                       1
nonlinear                    1
max. dimension               3
detected normal inq.           0
linear                       0
nonlinear                    0
Objective function          Linear

--------------------------------------------------------------
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. hessian                          26
--------------------------------------------------------------

Problem solved
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
Cone constraints:        not defined yet