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
Dfls Trust Region Update = Fast * d
Matrix Ordering = Auto * 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