NAG Library Manual, Mark 30.2
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NAG FL Interface Introduction
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
   Cone constraints:        not defined yet
   Quadratic 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
   Quadratic 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
   Quadratic 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
   Quadratic 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
     Task                          =            Minimize     * 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
     Nlp Factorization Method      =                Ma97     * 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
     Nldf Elastic Net Alpha        =         5.00000E-01     * d
     Nldf Elastic Net Beta         =         5.00000E-01     * 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
 
     Misqp Branch Bound Steps      =                 500     * d
     Misqp Branching Rule          =             Maximum     * d
     Misqp Continuous Trust Radius =         1.00000E+01     * d
     Misqp Descent                 =         5.00000E-02     * d
     Misqp Descent Factor          =         1.00000E-01     * d
     Misqp Feasible Steps          =                  10     * d
     Misqp Improved Bounds         =                  No     * d
     Misqp Integer Trust Radius    =         1.00000E+01     * d
     Misqp Iteration Limit         =                 500     * d
     Misqp Maximum Restarts        =                   2     * d
     Misqp Modify Hessian          =                 Yes     * d
     Misqp Monitor Frequency       =                   0     * d
     Misqp Node Selection          =         Depth First     * d
     Misqp Non Monotone            =                  10     * d
     Misqp Penalty                 =         1.00000E+03     * d
     Misqp Penalty Factor          =         1.00000E+01     * d
     Misqp Print Frequency         =                   1     * d
     Misqp Qp Accuracy             =         1.00000E-10     * d
     Misqp Scale Continuous Vars   =                 Yes     * d
     Misqp Scale Objective         =                 Yes     * d
     Misqp Scale Objective Bound   =         1.00000E+00     * d
     Misqp Stop Tolerance          =         1.00000E-05     * d
     Misqp Warm Starts             =                 100     * d

     Simplex Presolve              =                 Yes     * d
     Simplex Start Type            =                Cold     * d
     Simplex Strategy              =         Dual Serial     * d
     Simplex Random Seed           =                   0     * d
     Simplex Iteration Limit       =          2147483647     * d
     Simplex Primal Feasibility Tol=         1.00000E-07     * d
     Simplex Dual Feasibility Tol  =         1.00000E-07     * d
     Simplex Small Matrix Value    =         1.00000E-09     * 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. gradient                         39
   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
   Quadratic constraints:   not defined yet
   Matrix constraints:      2

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