E04VJF Example Program Results
NEA (the number of non-zero entries in A) = 4
I IAFUN(I) JAVAR(I) A(I)
---- -------- -------- -----------
1 4 1 -1.0000E+00
2 5 1 1.0000E+00
3 4 2 1.0000E+00
4 5 2 -1.0000E+00
NEG (the number of non-zero entries in G) = 10
I IGFUN(I) JGVAR(I)
---- -------- --------
1 1 1
2 2 1
3 3 1
4 1 2
5 2 2
6 3 2
7 6 3
8 6 4
9 1 3
10 2 4
Parameters
==========
Files
-----
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
--------------
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) 5
The SQP Method
--------------
Minimize............... Cold start............. Proximal Point method.. 1
Nonlinear objectiv vars 2 Objective Row.......... 6 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 Nonderiv. linesearch.. Derivative option...... 0
Major iterations limit. 1000 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
---------------------
Full-Memory Hessian.... Hessian updates........ 99999999 Hessian frequency...... 99999999
Hessian flush.......... 99999999
Nonlinear constraints
---------------------
Nonlinear constraints.. 3 Major feasibility tol.. 1.00E-06 Violation limit........ 1.00E+06
Nonlinear Jacobian vars 4
Miscellaneous
-------------
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 5 2 0 3 0
Columns 4 0 0 0 4
No. of matrix elements 12 Density 60.000
Biggest 1.0000E+00 (excluding fixed columns,
Smallest 0.0000E+00 free rows, and RHS)
No. of objective coefficients 0
Nonlinear constraints 3 Linear constraints 2
Nonlinear variables 4 Linear variables 0
Jacobian variables 4 Objective variables 2
Total constraints 5 Total variables 4
The user has defined 0 out of 10 first derivatives
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 14 1 3.0E+07 _ r
5 1 2 1.2E-03 2 4.0E+02 1.0E+00 1.7331709E+06 13 1 1.3E+07 5.1E+00 _n rl
6 2 1 1.3E-03 3 2.7E+02 5.5E-01 1.7301152E+06 13 5.1E+00 _s l
6 3 0 7.5E-03 4 8.8E+01 5.4E-01 8.8193389E+05 13 2.8E+00 _ l
6 4 0 2.3E-02 5 2.9E+01 5.3E-01 8.4262012E+05 13 2.8E+00 _ l
6 5 0 6.9E-02 6 8.9E+00 5.2E-01 7.3075574E+05 13 2.8E+00 _ l
7 6 1 2.2E-01 7 2.3E+00 8.0E+01 4.4817386E+05 13 1 1.2E+04 2.8E+00 _ l
8 7 1 8.3E-01 8 1.7E-01 9.2E+00 2.4331224E+04 13 1 9.5E+03 2.8E+00 _ l
9 8 1 1.0E+00 9 6.5E-03 4.0E+01 5.3127971E+03 13 1 1 1.3E+02 2.8E+00 _
10 9 1 1.0E+00 10 4.6E-03 1.2E+01 5.1602365E+03 13 1 9.4E+01 2.8E+00 _
11 10 1 1.0E+00 11 2.3E-04 6.2E-02 5.1265651E+03 13 1 9.6E+01 2.8E+00 _
12 11 1 1.0E+00 12 ( 1.3E-08) 2.9E-04 5.1264981E+03 13 1 1.2E+02 2.8E+00 _ c
13 11 2 1.0E+00 12 ( 1.3E-08) 2.7E-04 5.1264981E+03 13 1 1.2E+02 2.8E+00 _ c
14 12 1 1.0E+00 13 ( 5.5E-13) 7.0E-05 5.1264981E+03 13 1 9.5E+01 2.8E+00 _ c
15 13 1 1.0E+00 14 ( 1.8E-14)( 2.6E-09) 5.1264981E+03 13 1 9.5E+01 2.8E+00 _ c
E04VHU EXIT 0 -- finished successfully
E04VHU INFO 1 -- optimality conditions satisfied
Problem name
No. of iterations 15 Objective value 5.1264981096E+03
No. of major iterations 13 Linear objective 0.0000000000E+00
Penalty parameter 2.780E+00 Nonlinear objective 5.1264981096E+03
No. of calls to funobj 104 No. of calls to funcon 104
Calls with modes 1,2 (known g) 14 Calls with modes 1,2 (known g) 14
Calls for forward differencing 48 Calls for forward differencing 48
Calls for central differencing 24 Calls for central differencing 24
No. of superbasics 1 No. of basic nonlinears 3
No. of degenerate steps 0 Percentage 0.00
Max x 2 1.0E+03 Max pi 3 5.5E+00
Max Primal infeas 0 0.0E+00 Max Dual infeas 1 2.5E-08
Nonlinear constraint violn 1.5E-11
Name Objective Value 5.1264981096E+03
Status Optimal Soln Iteration 15 Superbasics 1
Objective (Min)
RHS
Ranges
Bounds
Section 1 - Rows
Number ...Row.. State ...Activity... Slack Activity ..Lower Limit. ..Upper Limit. .Dual Activity ..i
5 r 1 EQ -894.80000 0.00000 -894.80000 -894.80000 -4.38698 1
6 r 2 EQ -894.80000 0.00000 -894.80000 -894.80000 -4.10563 2
7 r 3 EQ -1294.80000 0.00000 -1294.80000 -1294.80000 -5.46328 3
8 r 4 BS -0.51511 0.03489 -0.55000 None . 4
9 r 5 BS 0.51511 1.06511 -0.55000 None . 5
Section 2 - Columns
Number .Column. State ...Activity... .Obj Gradient. ..Lower Limit. ..Upper Limit. Reduced Gradnt m+j
1 x 1 BS 0.11888 . -0.55000 0.55000 0.00000 6
2 x 2 BS -0.39623 . -0.55000 0.55000 0.00000 7
3 x 3 SBS 679.94532 4.38698 . 1200.00000 0.00000 8
4 x 4 BS 1026.06713 4.10563 . 1200.00000 0.00000 9
Final objective value = 5126.5
Optimal X = 0.12 -0.40 679.95 1026.07