nag_opt_sparse_nlp_solve (e04vhc) Example Program Results 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........ 2.05E-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 -------------- Minimize............... Cold start............. Proximal Point method.. 1 Nonlinear objectiv vars 4 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 Derivative linesearch.. Derivative option...... 1 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 2 Miscellaneous ------------- 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 ----------------- 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 2.23E-08 in constraint 7 The objective gradients seem to be OK. Gradient projected in one direction 0.00000000000E+00 Difference approximation 4.49060460280E-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 4 1 1 1.2E-03 2 4.0E+02 9.9E-01 9.6317131E+05 16 1 4.8E+06 2.8E+00 _n rl 5 2 1 1.3E-03 3 2.7E+02 5.5E-01 9.6122945E+05 16 2.8E+00 _s l 5 3 0 7.5E-03 4 8.8E+01 5.4E-01 9.4691061E+05 16 2.8E+00 _ l 5 4 0 2.3E-02 5 2.9E+01 5.3E-01 9.0468403E+05 16 2.8E+00 _ l 5 5 0 6.9E-02 6 8.9E+00 5.0E-01 7.8452897E+05 16 2.8E+00 _ l 6 6 1 2.2E-01 7 2.3E+00 5.5E+01 4.8112339E+05 16 1 8.7E+03 2.8E+00 _ l 7 7 1 8.3E-01 8 1.7E-01 4.2E+00 2.6898257E+04 16 1 7.6E+03 2.8E+00 _ l 8 8 1 1.0E+00 9 1.8E-02 8.7E+01 6.2192920E+03 15 1 1 1.2E+02 2.8E+00 _ 9 9 1 1.0E+00 10 1.7E-02 7.9E+00 5.4526185E+03 15 1 9.4E+01 2.8E+00 _ 10 10 1 1.0E+00 11 1.7E-04 9.6E-01 5.1266089E+03 15 1 1.0E+02 2.8E+00 _ 11 11 1 1.0E+00 12 1.7E-06 5.8E-02 5.1264988E+03 15 1 9.5E+01 2.8E+00 _ 12 12 1 1.0E+00 13 ( 1.2E-08) 6.9E-05 5.1264981E+03 15 1 9.5E+01 2.8E+00 _ 13 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 13 Objective value 5.1264981096E+03 No. of major iterations 13 Linear objective 4.0919702248E+03 Penalty parameter 6.029E+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 13 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