E04VKF Example Program Results
OPTIONS file
------------
Begin example options file
* Comment lines like this begin with an asterisk.
* Switch off output of timing information:
Timing level 0
* Allow elastic variables:
Elastic mode 1
* Set the feasibility tolerance:
Feasibility tolerance 1.0D-4
End
E04VKZ EXIT 100 -- finished successfully
E04VKZ INFO 101 -- OPTIONS file read
Option 'Elastic mode' has the value 1.
Option 'Feasibility tolerance' has the value 1.00000E-04.
Parameters
==========
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
-----------
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-04 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) 6
The SQP Method
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Minimize............... Cold start............. Proximal Point method.. 1
Nonlinear objectiv vars 4 Objective Row.......... 6 Function precision..... 1.72E-13
Unbounded step size.... 1.00E+10 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 option...... 1
Major iterations limit. 50 Linesearch tolerance... 0.90000 Verify level........... 0
Minor iterations limit. 500 Penalty parameter...... 0.00E+00 Major Print Level...... 1
Major optimality tol... 2.00E-06
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.. 3 Major feasibility tol.. 1.00E-06 Violation limit........ 1.00E+06
Nonlinear Jacobian vars 2
Miscellaneous
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LU factor tolerance.... 3.99 LU singularity tol..... 2.04E-11 Timing level........... 0
LU update tolerance.... 3.99 LU swap tolerance...... 1.03E-04 Debug level............ 0
LU partial pivoting... eps (machine precision) 1.11E-16 System information..... No
Matrix statistics
-----------------
Total Normal Free Fixed Bounded
Rows 6 2 1 3 0
Columns 4 0 0 0 4
No. of matrix elements 14 Density 58.333
Biggest 1.0000E+00 (excluding fixed columns,
Smallest 0.0000E+00 free rows, and RHS)
No. of objective coefficients 2
Biggest 3.0000E+00 (excluding fixed columns)
Smallest 2.0000E+00
Nonlinear constraints 3 Linear constraints 3
Nonlinear variables 4 Linear variables 0
Jacobian variables 2 Objective variables 4
Total constraints 6 Total variables 4
The user has defined 8 out of 8 first derivatives
Cheap test of user-supplied problem derivatives...
The constraint gradients seem to be OK.
--> The largest discrepancy was 2.20E-08 in constraint 6
The objective gradients seem to be OK.
Gradient projected in one direction 0.00000000000E+00
Difference approximation 4.48709939860E-21
Itns Major Minors Step nCon Feasible Optimal MeritFunction L+U BSwap nS condHz Penalty
3 0 3 1 8.0E+02 1.0E+00 0.0000000E+00 17 1 1.7E+07 _ r
5 1 2 1.2E-03 2 4.0E+02 9.9E-01 9.6317131E+05 16 1 4.8E+06 2.8E+00 _n rl
6 2 1 1.3E-03 3 2.7E+02 5.5E-01 9.6122945E+05 16 2.8E+00 _s l
6 3 0 7.5E-03 4 8.8E+01 5.4E-01 9.4691061E+05 16 2.8E+00 _ l
6 4 0 2.3E-02 5 2.9E+01 5.3E-01 9.0468403E+05 16 2.8E+00 _ l
6 5 0 6.9E-02 6 8.9E+00 5.0E-01 7.8452897E+05 16 2.8E+00 _ l
7 6 1 2.2E-01 7 2.3E+00 5.5E+01 4.8112339E+05 16 1 8.7E+03 2.8E+00 _ l
8 7 1 8.3E-01 8 1.7E-01 4.2E+00 2.6898257E+04 16 1 7.6E+03 2.8E+00 _ l
9 8 1 1.0E+00 9 1.8E-02 8.7E+01 6.2192920E+03 15 1 1 1.2E+02 2.8E+00 _
10 9 1 1.0E+00 10 1.7E-02 7.9E+00 5.4526185E+03 15 1 9.4E+01 2.8E+00 _
11 10 1 1.0E+00 11 1.7E-04 9.6E-01 5.1266089E+03 15 1 1.0E+02 2.8E+00 _
12 11 1 1.0E+00 12 1.7E-06 5.8E-02 5.1264988E+03 15 1 9.5E+01 2.8E+00 _
13 12 1 1.0E+00 13 ( 1.2E-08) 6.9E-05 5.1264981E+03 15 1 9.5E+01 2.8E+00 _
14 13 1 1.0E+00 14 ( 6.7E-15)( 3.0E-09) 5.1264981E+03 15 1 9.5E+01 6.0E+00 _
E04VHU EXIT 0 -- finished successfully
E04VHU INFO 1 -- optimality conditions satisfied
Problem name
No. of iterations 14 Objective value 5.1264981096E+03
No. of major iterations 13 Linear objective 4.0919702248E+03
Penalty parameter 6.038E+00 Nonlinear objective 1.0345278848E+03
No. of calls to funobj 15 No. of calls to funcon 15
No. of superbasics 1 No. of basic nonlinears 3
No. of degenerate steps 0 Percentage 0.00
Max x 4 1.0E+03 Max pi 3 5.5E+00
Max Primal infeas 0 0.0E+00 Max Dual infeas 1 4.6E-08
Nonlinear constraint violn 5.7E-12
Name Objective Value 5.1264981096E+03
Status Optimal Soln Iteration 14 Superbasics 1
Objective (Min)
RHS
Ranges
Bounds
Section 1 - Rows
Number ...Row.. State ...Activity... Slack Activity ..Lower Limit. ..Upper Limit. .Dual Activity ..i
5 NlnCon 1 EQ -894.80000 0.00000 -894.80000 -894.80000 -4.38698 1
6 NlnCon 2 EQ -894.80000 0.00000 -894.80000 -894.80000 -4.10563 2
7 NlnCon 3 EQ -1294.80000 0.00000 -1294.80000 -1294.80000 -5.46328 3
8 LinCon 1 BS -0.51511 0.03489 -0.55000 None . 4
9 LinCon 2 BS 0.51511 1.06511 -0.55000 None . 5
10 Objectiv BS 4091.97022 4091.97022 None None -1.0 6
Section 2 - Columns
Number .Column. State ...Activity... .Obj Gradient. ..Lower Limit. ..Upper Limit. Reduced Gradnt m+j
1 X1 BS 0.11888 . -0.55000 0.55000 0.00000 7
2 X2 BS -0.39623 . -0.55000 0.55000 0.00000 8
3 X3 SBS 679.94532 4.38698 . 1200.00000 0.00000 9
4 X4 BS 1026.06713 4.10563 . 1200.00000 0.00000 10
Final objective value = 5126.5
Optimal X = 0.12 -0.40 679.95 1026.07