E04WDF Example Program Results
Parameters
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Files
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Solution file.......... 0 Old basis file ........ 0 (Print file)........... 6
Insert file............ 0 New basis file ........ 0 (Summary file)......... 0
Punch file............. 0 Backup basis file...... 0
Load file.............. 0 Dump file.............. 0
Frequencies
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Print frequency........ 100 Check frequency........ 60 Save new basis map..... 100
Summary frequency...... 100 Factorization frequency 50 Expand frequency....... 10000
QP subproblems
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QPsolver Cholesky......
Scale tolerance........ 0.900 Minor feasibility tol.. 1.00E-06 Iteration limit........ 10000
Scale option........... 0 Minor optimality tol.. 1.00E-06 Minor print level...... 1
Crash tolerance........ 0.100 Pivot tolerance........ 2.04E-11 Partial price.......... 1
Crash option........... 3 Elastic weight......... 1.00E+04 Prtl price section ( A) 4
New superbasics........ 99 Prtl price section (-I) 3
The SQP Method
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Minimize............... Cold start............. Proximal Point method.. 1
Nonlinear objectiv vars 4 Major optimality tol... 2.00E-06 Function precision..... 1.72E-13
Unbounded step size.... 1.00E+20 Superbasics limit...... 4 Difference interval.... 4.15E-07
Unbounded objective.... 1.00E+15 Reduced Hessian dim.... 4 Central difference int. 5.57E-05
Major step limit....... 2.00E+00 Derivative linesearch.. Derivative level....... 3
Major iterations limit. 1000 Linesearch tolerance... 0.90000 Verify level........... 0
Minor iterations limit. 500 Penalty parameter...... 0.00E+00 Major Print Level...... 1
Hessian Approximation
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Full-Memory Hessian.... Hessian updates........ 99999999 Hessian frequency...... 99999999
Hessian flush.......... 99999999
Nonlinear constraints
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Nonlinear constraints.. 2 Major feasibility tol.. 1.00E-06 Violation limit........ 1.00E+06
Nonlinear Jacobian vars 4
Miscellaneous
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LU factor tolerance.... 1.10 LU singularity tol..... 2.04E-11 Timing level........... 0
LU update tolerance.... 1.10 LU swap tolerance...... 1.03E-04 Debug level............ 0
LU partial pivoting... eps (machine precision) 1.11E-16 System information..... No
Matrix statistics
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Total Normal Free Fixed Bounded
Rows 3 3 0 0 0
Columns 4 0 0 0 4
No. of matrix elements 12 Density 100.000
Biggest 1.0000E+00 (excluding fixed columns,
Smallest 0.0000E+00 free rows, and RHS)
No. of objective coefficients 0
Nonlinear constraints 2 Linear constraints 1
Nonlinear variables 4 Linear variables 0
Jacobian variables 4 Objective variables 4
Total constraints 3 Total variables 4
The user has defined 8 out of 8 constraint gradients.
The user has defined 4 out of 4 objective gradients.
Cheap test of user-supplied problem derivatives...
The constraint gradients seem to be OK.
--> The largest discrepancy was 1.84E-07 in constraint 6
The objective gradients seem to be OK.
Gradient projected in one direction 4.99993000077E+00
Difference approximation 4.99993303560E+00
Itns Major Minors Step nCon Feasible Optimal MeritFunction L+U BSwap nS condHz Penalty
2 0 2 1 1.7E+00 2.8E+00 1.6000000E+01 7 2 1.0E+00 _ r
4 1 2 1.0E+00 2 1.3E-01 3.2E-01 1.7726188E+01 8 1 6.2E+00 8.3E-02 _n r
5 2 1 1.0E+00 3 3.7E-02 1.7E-01 1.7099571E+01 7 1 2.0E+00 8.3E-02 _s
6 3 1 1.0E+00 4 2.2E-02 1.1E-02 1.7014005E+01 7 1 1.8E+00 8.3E-02 _
7 4 1 1.0E+00 5 1.5E-04 6.0E-04 1.7014018E+01 7 1 1.8E+00 9.2E-02 _
8 5 1 1.0E+00 6 ( 3.3E-07) 2.3E-05 1.7014017E+01 7 1 1.9E+00 3.6E-01 _
9 6 1 1.0E+00 7 ( 4.2E-10)( 2.4E-08) 1.7014017E+01 7 1 1.9E+00 3.6E-01 _
E04WDM EXIT 0 -- finished successfully
E04WDM INFO 1 -- optimality conditions satisfied
Problem name NLP
No. of iterations 9 Objective value 1.7014017287E+01
No. of major iterations 6 Linear objective 0.0000000000E+00
Penalty parameter 3.599E-01 Nonlinear objective 1.7014017287E+01
No. of calls to funobj 8 No. of calls to funcon 8
No. of superbasics 1 No. of basic nonlinears 2
No. of degenerate steps 0 Percentage 0.00
Max x 2 4.7E+00 Max pi 2 5.5E-01
Max Primal infeas 0 0.0E+00 Max Dual infeas 3 4.8E-08
Nonlinear constraint violn 2.7E-09
Variable State Value Lower bound Upper bound Lagr multiplier Slack
variable 1 LL 1.000000 1.000000 5.000000 1.087871 .
variable 2 FR 4.743000 1.000000 5.000000 . 0.2570
variable 3 FR 3.821150 1.000000 5.000000 . 1.179
variable 4 FR 1.379408 1.000000 5.000000 . 0.3794
Linear constrnt State Value Lower bound Upper bound Lagr multiplier Slack
lincon 1 FR 10.94356 None 20.00000 . 9.056
Nonlin constrnt State Value Lower bound Upper bound Lagr multiplier Slack
nlncon 1 UL 40.00000 None 40.00000 -0.1614686 -0.2700E-08
nlncon 2 LL 25.00000 25.00000 None 0.5522937 -0.2215E-08
Final objective value = 17.014
Optimal X = 1.00 4.74 3.82 1.38