nag_opt_sparse_convex_qp_solve (e04nqc) 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
LP/QP Parameters
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Minimize............... QPsolver Cholesky...... Cold start.............
Scale tolerance........ 0.900 Feasibility tolerance.. 1.00E-06 Iteration limit........ 10000
Scale option........... 2 Optimality tolerance... 1.00E-06 Print level............ 1
Crash tolerance........ 0.100 Pivot tolerance........ 2.05E-11 Partial price.......... 1
Crash option........... 3 Elastic weight......... 1.00E+00 Prtl price section ( A) 7
Elastic mode........... 1 Elastic objective...... 1 Prtl price section (-I) 8
QP objective
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Objective variables.... 7 Hessian columns........ 7 Superbasics limit...... 7
Nonlin Objective vars.. 7 Unbounded step size.... 1.00E+20
Linear Objective vars.. 0
Miscellaneous
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LU factor tolerance.... 3.99 LU singularity tol..... 2.05E-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
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Total Normal Free Fixed Bounded
Rows 8 5 1 1 1
Columns 7 2 0 0 5
No. of matrix elements 48 Density 85.714
Biggest 1.0000E+00 (excluding fixed columns,
Smallest 1.0000E-02 free rows, and RHS)
No. of objective coefficients 7
Biggest 2.0000E+03 (excluding fixed columns)
Smallest 2.0000E+02
Nonlinear constraints 0 Linear constraints 8
Nonlinear variables 7 Linear variables 0
Jacobian variables 0 Objective variables 7
Total constraints 8 Total variables 7
Itn 1: Feasible linear constraints
E04NQT EXIT 0 -- finished successfully
E04NQT INFO 1 -- optimality conditions satisfied
Problem name
No. of iterations 9 Objective value -1.8477846771E+06
No. of Hessian products 16 Objective row -2.9886903537E+06
Quadratic objective 1.1409056766E+06
No. of superbasics 2 No. of basic nonlinears 4
No. of degenerate steps 0 Percentage 0.00
Max x (scaled) 3 2.4E-01 Max pi (scaled) 6 4.7E+07
Max x 3 6.5E+02 Max pi 7 1.5E+04
Max Prim inf(scaled) 0 0.0E+00 Max Dual inf(scaled) 6 1.1E-08
Max Primal infeas 0 0.0E+00 Max Dual infeas 9 6.4E-12
Name Objective Value -1.8477846771E+06
Status Optimal Soln Iteration 9 Superbasics 2
Section 1 - Rows
Number ...Row.. State ...Activity... Slack Activity ..Lower Limit. ..Upper Limit. .Dual Activity ..i
8 ..ROW1.. EQ 2000.00000 . 2000.00000 2000.00000 -12900.76766 1
9 ..ROW2.. BS 49.23160 -10.76840 None 60.00000 0.00000 2
10 ..ROW3.. UL 100.00000 . None 100.00000 -2324.86620 3
11 ..ROW4.. BS 32.07187 -7.92813 None 40.00000 . 4
12 ..ROW5.. BS 14.55719 -15.44281 None 30.00000 . 5
13 ..ROW6.. LL 1500.00000 . 1500.00000 None 14454.60290 6
14 ..ROW7.. LL 250.00000 . 250.00000 300.00000 14580.95432 7
15 ..COST.. BS -2988690.35370 -2988690.35370 None None -1.0 8
Section 2 - Columns
Number .Column. State ...Activity... .Obj Gradient. ..Lower Limit. ..Upper Limit. Reduced Gradnt m+j
1 ...X1... LL . -200.00000 . 200.00000 2360.67253 9
2 ...X2... BS 349.39923 -1301.20153 . 2500.00000 -0.00000 10
3 ...X3... SBS 648.85342 -356.59829 400.00000 800.00000 0.00000 11
4 ...X4... SBS 172.84743 -356.59829 100.00000 700.00000 -0.00000 12
5 ...X5... BS 407.52089 -1184.95822 . 1500.00000 -0.00000 13
6 ...X6... BS 271.35624 1242.75804 . None -0.00000 14
7 ...X7... BS 150.02278 1242.75804 . None 0.00000 15
Final objective value = -1.848e+06
Optimal X = 0.00 349.40 648.85 172.85 407.52 271.36 150.02