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 Subproblem Max Nodes = 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 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
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E04SV, NLP-SDP Solver (Pennon)
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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
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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