Output from FIND_GLOBAL_MIN on 05/05/2012 at 03:43:55. Version for the system is: March 13, 2009 Codelist file name is: ex5_2_4_sourceG.CDL Box data file name is: ex5_2_4_source.DT1 Initial box: [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 100. ] [ 0.00 , 200. ], [ 0.00 , 100. ] [ 0.00 , 200. ] BOUND_CONSTRAINT: F F F F F F F F F F F F F F --------------------------------------- CONFIGURATION VALUES: EPS_DOMAIN: 0.1000D-07 MAXITR: 500000 SMALLEST_LIST_BOX_SIZE = 0.0000D+00 A_PRIORI_UPPER_BOUND (on global optimum): 0.180+309 MAX_CPU_SECONDS: 0.720E+04 MAX_LP_PRE: 10000000 ALSO_PRINT_TO_TERMINAL F NO_ABSOLUTE_VALUE_IN_MINIMAX F MAX_PT_SOLVER_ITER 3000 MAX_SMALL_BOXES 2000 MAX_BEFORE_AMALGAMATE 200 DO_INTERVAL_NEWTON: T QUADRATIC: T FULL_SPACE: F VERY_GOOD_INITIAL_GUESS: F USE_SUBSIT: T OUTPUT UNIT: 7 PRINT_LENGTH: 3 USE_INTRINSIC_PRINTING: T PHI_MUST_CONVERGE: T EQ_CNS_MUST_CONVERGE: T INEQ_CNS_MUST_CONVERGE: T ALLOW_EPSILON_APPROXIMATE: F USES_INTERMEDIATE_VARIABLES: F PHI_THICKNESS_FACTOR: 0.500 EQ_CNS_THICKNESS_FACTOR: 0.500 INEQ_CNS_THICKNESS_FACTOR: 0.500 PHI_MUST_CONVERGE: T EQ_CNS_MUST_CONVERGE: T INEQ_CNS_MUST_CONVERGE: T PHI_CONVERGENCE_FACTOR: 0.100E-13 EQ_CNS_CONVERGENCE_FACTOR: 0.100E-13 INEQ_CNS_CONVERGENCE_FACTOR: 0.100E-13 CONTINUITY_ACROSS_BRANCHES: F SINGULAR_EXPANSION_FACTOR: 10.0 HEURISTIC PARAMETER ALPHA: 0.500 APPROX_OPT_BEFORE_BISECTION: F APPROX_OPTIMIZER_TYPE 7 USE_LP: T ITERATE__LP: F EPS_LP_FIT: 1.00000000000000002E-002 USE_EPPERLY_SPLIT: 0 PRINTING_IN_SPLIT 0 USE_REDUCED_SPACE: F REDUCED_IN_BISECTION: T USE_TAYLOR_EQUALITY_CONSTRAINTS F USE_TAYLOR_INEQ_CONSTRAINTS F USE_TAYLOR_OBJECTIVE F USE_TAYLOR_EQ_CNS_GRD F USE_TAYLOR_GRAD F USE_TAYLOR_INEQ_CNS_GRD F USE_TAYLOR_REDUCED_INEWTON F COSY_POLYNOMIAL_ORDER 5 LEAST_SQUARES_FUNCTIONS: F NONLINEAR_SYSTEM: F UNCONSTRAINED_MINIMAX: F NO_ABSOLUTE_VALUE_IN_MINIMAX: F DO_INFEASIBILITY_CHECK: T DO_PIVOTING: T DO_INV_MID: T TRY_C_LP_HEURISTIC: 10000000000.000000 REUSE_PRECONDITIONERS: T ORDERED_LIST_IN_COMPLEMENTATION 1 DO_PROBE: F DO_PROBE_TESTS_3_AND_4: F USE_INEQ_PERTURB_FOR_FEAS: F DO_SPLITS_IN_SUBSIT F PRINTING_IN_VALIDATE_FJ: 0 PRINT_SUBSIT: 0 ALSO_PRINT_TO_TERMINAL F C-LP is used for computing C-LP preconditioners. UNCONSTRAINED_MINIMAX F NO_ABSOLUTE_VALUE_IN_MINIMAX F MINIMAX_FORMULATION_2 T C_LP_DENSE, Manuel Novoa's special routine, was used to compute LP preconditioners. LIST OF SMALL BOXES: Box no.: 1 Box coordinates: [ 0.00 , 0.150E-02 ], [ 0.499 , 0.501 ] [ 0.499 , 0.501 ], [ 0.00 , 0.150E-02 ] [ 99.9 , 100. ], [ 0.00 , 0.150E-02 ] [ 99.9 , 100. ] PHI: [ -454. , -445. ] Box contains the following approximate root: -0.100E-07, 0.500 , 0.500 , -0.996E-08, 100. , 0.100E-07 100. OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ -450. , -450. ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.433E-03, 0.433E-03 ] Fritz John multipliers U: [ 0.433E-03, 0.433E-03 ], [ 0.00 , 1.00 ] [ 0.865E-03, 0.866E-03 ], [ 0.00 , 0.890E-03 ] [ 0.260E-02, 0.260E-02 ], [ 0.865E-01, 0.866E-01 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.169E-02, 0.307E-02 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 0.445E-03 ] [ 0.00 , 0.500 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ] Fritz John multipliers V: [ -0.952 , -0.952 ] INEQ_CERT_FEASIBLE: F T F F F F T T T T T F T T T F T T T NIN_POSS_BINDING: 7 ------------------------------------------------- Box no.: 2 Box coordinates: [ 0.998 , 1.00 ], [ 0.00 , 0.150E-02 ] [ 0.00 , 0.150E-02 ], [ 50.0 , 50.1 ] [ 0.00 , 0.150E-02 ], [ 49.9 , 50.0 ] [ 0.00 , 0.150E-02 ] PHI: [ -101. , -97.5 ] Box contains the following approximate root: 1.00 , -0.100E-07, -0.154E-12, 50.0 , -0.999E-08, 50.0 0.500E-07 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ -100. , -100. ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.00 , 0.118E-02 ] Fritz John multipliers U: [ 0.00 , 1.00 ], [ 0.00 , 0.116E-02 ] [ 0.00 , 1.00 ], [ 0.00 , 0.458E-02 ] [ 0.00 , 0.596 ], [ 0.00 , 1.00 ] [ 0.00 , 0.547E-01 ], [ 0.00 , 0.119 ] [ 0.00 , 1.00 ], [ 0.00 , 0.573E-01 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 0.220E-01 ], [ 0.00 , 0.896 ] [ 0.00 , 1.00 ], [ 0.00 , 0.134E-01 ] [ 0.00 , 0.500 ], [ 0.00 , 0.298 ] [ 0.00 , 1.00 ] Fritz John multipliers V: [ -1.00 , 0.411E-01 ] INEQ_CERT_FEASIBLE: T F T F F T T F T F T T T F T T T F T NIN_POSS_BINDING: 7 ------------------------------------------------- Box no.: 3 Box coordinates: [ 0.955 , 0.957 ], [ 0.138E-01, 0.158E-01 ] [ 0.286E-01, 0.306E-01 ], [ 50.0 , 50.1 ] [ 0.00 , 0.150E-02 ], [ 41.1 , 41.2 ] [ 0.00 , 0.150E-02 ] PHI: [ -90.2 , -86.2 ] Box contains the following approximate root: 1.00 , -0.100E-07, -0.154E-12, 50.0 , -0.999E-08, 50.0 0.500E-07 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ -100. , -100. ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.00 , 0.760E-16 ] Fritz John multipliers U: [ 0.00 , 1.00 ], [ 0.00 , 0.225E-02 ] [ 0.00 , 1.00 ], [ 0.00 , 0.742E-16 ] [ 0.332 , 0.348 ], [ 0.00 , 1.00 ] [ 0.00 , 0.414 ], [ 0.00 , 0.904E-13 ] [ 0.00 , 1.00 ], [ 0.00 , 0.854E-13 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 0.220E-01 ], [ 0.478 , 0.502 ] [ 0.00 , 1.00 ], [ 0.00 , 0.134E-01 ] [ 0.00 , 0.500 ], [ 0.166 , 0.174 ] [ 0.00 , 1.00 ] Fritz John multipliers V: [ -0.683E-13, 0.262E-13 ] INEQ_CERT_FEASIBLE: T T T F F T T F T F T T T F T T T F T NIN_POSS_BINDING: 6 ------------------------------------------------- LIST OF BOXES CONTAINING VERIFIED FEASIBLE POINTS: Box no.: 1 Box coordinates: [ 0.518E-01, 0.538E-01 ], [ 0.893 , 0.895 ] [ 0.518E-01, 0.538E-01 ], [ 50.0 , 50.1 ] [ 184. , 184. ], [ 50.0 , 50.1 ] [ 15.8 , 15.9 ] PHI: [ 360. , 378. ] Box contains the following approximate root: 0.528E-01, 0.894 , 0.528E-01, 50.0 , 184. , 50.0 15.8 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 369. , 369. ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.00 , 1.00 ] Fritz John multipliers U: [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ] Fritz John multipliers V: [ -1.00 , 1.00 ] INEQ_CERT_FEASIBLE: F F F F F F F F F F F F F F F F F F F NIN_POSS_BINDING: 19 ------------------------------------------------- ALGORITHM COULD NOT COMPLETE WITH LESS THAN 500000 BOXES CONSIDERED. Number of boxes that have not yet been processed: 130890 Number of bisections: 426977 No. dense interval residual evaluations -- gradient code list: 6949334 Number of orig. system inverse midpoint preconditioner rows: 8177511 Number of orig. system C-LP preconditioner rows: 3507973 Number of solutions for a component in the expanded system: 7236221 Total number of forward_substitutions: 28744190 Number of Gauss--Seidel steps on the dense system: 13349486 Number point dense residual evaluations, gradient codelist: 3404 Number of gradient evaluations from a gradient code list: 2350341 Total number of dense slope matrix evaluations: 9720164 Total number second-order interval evaluations of the original function: 1085846 Total number dense interval constraint evaluations: 211091910 Total number dense interval constraint gradient component evaluations: 849125060 Total number dense point constraint gradient component evaluations: 1072456 Total number dense interval reduced gradient evaluations: 4961720 Total number of calls to FRITZ_JOHN_RESIDUALS: 1247386 Number of times a box was rejected because the constraints were not satisfied: 1636 Number of times a box was rejected because the gradient or reduced gradient did not contain zero: 13911 Number of times a box was rejected due to infeasibility in LP_FILTER: 735 Average number of overall loop iterations in each call to the reduced interval Newton method): 2.61 Number of times a box was rejected in the interval Newton method due to an empty intersection: 3761 Number of times the interval Newton method made a coordinate interval smaller: 1556576 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 515240 Number of times a pivoting preconditioner was successful after the first sweep: 231738 Number of times a midpoint matrix was factored: 832072 Total number of times the reduced interval Newton method was tried: 497660 Number of times an inverse midpoint preconditioner led to improvement or rejection: 305975 Number of times a C LP preconditioner led to improvement or rejection: 739122 Number of times computing a C_LP failed 239 N_C_LP_INFEASIBLE = 220716 N_REJECT_WITH_LP filter = 894 N_LPF_INF_OR_UNB = 220700 Number of possible splits as detected by the pivoting preconditioner: 1233474 Total time spent in the LP filter (creating and solving the LP): 0.145E+04 Total time spent in subsit (constraint propagation): 10.8 Total time spent in reduced_interval_Newton (iteration to reduce the box): 0.128E+04 Total time spent actually solving the linear relaxations: 0.131E+04 Total time spent doing linear algebra (preconditioners and solution processes): 794. Total time spent running the approximate optimizer: 0.800E-01 LIST_BOOKKEEPING_TIME: 0.127E+04 FUNCTION_EVALUATION_TIME (in forward_substitution): 216. Time spent setting up pivoting preconditioners: 86.1 Time spent computing pivoting preconditioners: 60.3 Time spent computing LP preconditioners: 179. Time spent computing inverse midpoint preconditioners: 51.2 Number of times MAXIT was exceeded in C_LP_DENSE: 7096 Number of unbounded problems found in C_LP_DENSE: 239 Number of times the approximate solver was called: 252 Number Fritz-John matrix evaluations: 1233474 Number of times SUBSIT decreased one or more coordinate widths: 39637 Number of times SUBSIT rejected a box: 1358 Number times a box was rejected due infeasible inequality constraints: 51712 Total number of boxes processed in loop: 500000 N_FINDOPT_SUCCESS = 249 BEST_ESTIMATE: 369. Overall CPU time: 0.431E+04 CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 0.128E+04 =================================================== =================================================== Number of boxes in the list with proven feasible points: 1 Number of boxes in the list of other small boxes: 3 Number of unfathomed boxes: 130890 Interval hull of the boxes verified to contain feasible points or critical points: [ 0.518E-01, 0.538E-01 ], [ 0.893 , 0.895 ] [ 0.518E-01, 0.538E-01 ], [ 50.0 , 50.1 ] [ 184. , 184. ], [ 50.0 , 50.1 ] [ 15.8 , 15.9 ] Interval hull of the small unverified boxes: [ 0.00 , 1.00 ], [ 0.00 , 0.501 ] [ 0.00 , 0.501 ], [ 0.00 , 50.1 ] [ 0.00 , 100. ], [ 0.00 , 50.0 ] [ 0.00 , 100. ] Interval hull of the unfathomed boxes: [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 100. ] [ 0.00 , 200. ], [ 0.00 , 100. ] [ 0.00 , 115. ] Rigorously verified bounds on the optimum, provided an optimum exists: [ -454. , 369. ] FIRST UNFINISHED BOX: Box coordinates: [ 0.999 , 0.999 ], [ 0.199E-04, 0.217E-04 ] [ 0.496E-03, 0.498E-03 ], [ 50.1 , 50.1 ] [ 0.00 , 0.276-306 ], [ 49.9 , 49.9 ] [ 0.00 , 0.445-307 ] PHI: [ -100. , -100. ] Box does not contain an approximate root. Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.00 , 0.235E-17 ] Fritz John multipliers U: [ 0.00 , 1.00 ], [ 0.00 , 0.261E-17 ] [ 0.00 , 1.00 ], [ 0.00 , 0.116E-16 ] [ 0.333 , 0.333 ], [ 0.00 , 1.00 ] [ 0.00 , 0.578E-01 ], [ 0.00 , 0.876E-16 ] [ 0.00 , 1.00 ], [ 0.00 , 0.643E-01 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 0.220E-01 ], [ 0.500 , 0.500 ] [ 0.00 , 1.00 ], [ 0.00 , 0.134E-01 ] [ 0.00 , 0.500 ], [ 0.167 , 0.167 ] [ 0.00 , 1.00 ] Fritz John multipliers V: [ -0.925E-18, 0.925E-18 ] INEQ_CERT_FEASIBLE: T T T F F T T T T T T T T F T T T F T NIN_POSS_BINDING: 4 LAST UNFINISHED BOX: Box coordinates: [ 0.518E-01, 0.538E-01 ], [ 0.893 , 0.895 ] [ 0.518E-01, 0.538E-01 ], [ 50.0 , 50.1 ] [ 184. , 184. ], [ 50.0 , 50.1 ] [ 0.00 , 15.8 ] PHI: [ 360. , 457. ] Box contains the following approximate root: 0.528E-01, 0.894 , 0.528E-01, 50.0 , 184. , 50.0 7.91 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 409. , 409. ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.00 , 1.00 ] Fritz John multipliers U: [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ] Fritz John multipliers V: [ -1.00 , 1.00 ] INEQ_CERT_FEASIBLE: F F F F F F F F F F F F F F F F F F F NIN_POSS_BINDING: 19 Total volume of the boxes that have not yet been processed: 382960.68409995839