Output from FIND_GLOBAL_MIN on 05/07/2012 at 22:25:02. Version for the system is: March 13, 2009 Codelist file name is: ex14_2_6_sourceG.CDL Box data file name is: ex14_2_6_source.DT1 Initial box: [ 0.100E-05, 1.00 ], [ 0.100E-05, 1.00 ] [ 0.100E-05, 1.00 ], [ 40.0 , 90.0 ] [ 0.00 , 0.100E+05 ] BOUND_CONSTRAINT: 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. THERE WERE NO BOXES IN THE LIST OF SMALL BOXES. LIST OF BOXES CONTAINING VERIFIED FEASIBLE POINTS: Box no.: 1 Box coordinates: [ 0.332 , 0.334 ], [ 0.332 , 0.334 ] [ 0.332 , 0.334 ], [ 72.6 , 72.7 ] [ 0.347E+04, 0.348E+04 ] PHI: [ 0.347E+04, 0.348E+04 ] Box contains the following approximate root: 0.333 , 0.333 , 0.333 , 72.6 , 0.348E+04 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 0.348E+04, 0.348E+04 ] 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 ] 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 NIN_POSS_BINDING: 15 ------------------------------------------------- ALGORITHM COULD NOT COMPLETE IN 0.7200D+04 SECONDS OF CPU TIME. Number of boxes that have not yet been processed: 132321 Number of bisections: 296651 No. dense interval residual evaluations -- gradient code list: 4717536 Number of orig. system inverse midpoint preconditioner rows: 8348456 Number of orig. system C-LP preconditioner rows: 2690498 Number of solutions for a component in the expanded system: 348453823 Total number of forward_substitutions: 15127644 Number of Gauss--Seidel steps on the dense system: 11338143 Number point dense residual evaluations, gradient codelist: 14 Number of gradient evaluations from a gradient code list: 1675848 Total number of dense slope matrix evaluations: 4702691 Total number second-order interval evaluations of the original function: 593316 Total number dense interval constraint evaluations: 115765759 Total number dense interval constraint gradient component evaluations: 331317850 Total number dense point constraint gradient component evaluations: 1440 Total number dense interval reduced gradient evaluations: 3287500 Total number of calls to FRITZ_JOHN_RESIDUALS: 821875 Number of times a box was rejected due to infeasibility in LP_FILTER: 4 Average number of overall loop iterations in each call to the reduced interval Newton method): 2.57 Number of times a box was rejected in the interval Newton method due to an empty intersection: 6 Number of times the interval Newton method made a coordinate interval smaller: 789097 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 448380 Number of times a pivoting preconditioner was successful after the first sweep: 291465 Number of times a midpoint matrix was factored: 597373 Total number of times the reduced interval Newton method was tried: 335462 Number of times an inverse midpoint preconditioner led to improvement or rejection: 278933 Number of times a C LP preconditioner led to improvement or rejection: 61790 Number of times computing a C_LP failed 29 N_C_LP_INFEASIBLE = 306718 N_REJECT_WITH_LP filter = 4 N_LPF_INF_OR_UNB = 306716 Number of possible splits as detected by the pivoting preconditioner: 821875 Total time spent in the LP filter (creating and solving the LP): 0.324E+04 Total time spent in subsit (constraint propagation): 163. Total time spent in reduced_interval_Newton (iteration to reduce the box): 0.118E+04 Total time spent searching for "D" in the LP filter: 27.3 Total time spent actually solving the linear relaxations: 0.289E+04 Total time spent doing linear algebra (preconditioners and solution processes): 520. LIST_BOOKKEEPING_TIME: 0.155E+04 FUNCTION_EVALUATION_TIME (in forward_substitution): 966. Time spent setting up pivoting preconditioners: 43.4 Time spent computing pivoting preconditioners: 50.6 Time spent computing LP preconditioners: 98.2 Time spent computing inverse midpoint preconditioners: 29.1 Number of times MAXIT was exceeded in C_LP_DENSE: 22009 Number of unbounded problems found in C_LP_DENSE: 29 Number of times the approximate solver was called: 1 Number Fritz-John matrix evaluations: 821875 Number of times SUBSIT decreased one or more coordinate widths: 5825 Number of times SUBSIT rejected a box: 76146 Number times a box was rejected due infeasible inequality constraints: 38808 Total number of boxes processed in loop: 411614 N_FINDOPT_SUCCESS = 1 BEST_ESTIMATE: 0.348E+04 Overall CPU time: 0.720E+04 CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 0.118E+04 =================================================== =================================================== Number of boxes in the list with proven feasible points: 1 Number of boxes in the list of other small boxes: 0 Number of unfathomed boxes: 132321 Interval hull of the boxes verified to contain feasible points or critical points: [ 0.332 , 0.334 ], [ 0.332 , 0.334 ] [ 0.332 , 0.334 ], [ 72.6 , 72.7 ] [ 0.347E+04, 0.348E+04 ] Interval hull of the unfathomed boxes: [ 0.100E-05, 1.00 ], [ 0.100E-05, 1.00 ] [ 0.100E-05, 1.00 ], [ 40.0 , 90.0 ] [ 0.00 , 0.500E+04 ] Rigorously verified bounds on the optimum, provided an optimum exists: [ 0.347E+04, 0.348E+04 ] FIRST UNFINISHED BOX: Box coordinates: [ 0.162E-01, 0.164E-01 ], [ 0.602 , 0.602 ] [ 0.382 , 0.382 ], [ 61.8 , 61.8 ] [ 0.00 , 0.298E-03 ] PHI: [ 0.00 , 0.298E-03 ] Box does not contain an approximate root. Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.500 , 0.500 ] Fritz John multipliers U: [ 0.00 , 0.504 ], [ 0.00 , 0.504 ] [ 0.00 , 0.504 ], [ 0.00 , 0.504 ] [ 0.00 , 0.504 ], [ 0.00 , 0.504 ] [ 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 , 0.156 ], [ 0.00 , 0.156 ] [ 0.00 , 0.504 ] Fritz John multipliers V: [ -0.181E-01, 0.181E-01 ] INEQ_CERT_FEASIBLE: F F F F F F T T T T T T T T F NIN_POSS_BINDING: 7 LAST UNFINISHED BOX: Box coordinates: [ 0.100E-05, 0.332 ], [ 0.500 , 0.875 ] [ 0.125 , 0.250 ], [ 40.0 , 90.0 ] [ 0.250E+04, 0.500E+04 ] PHI: [ 0.250E+04, 0.500E+04 ] Box does not contain an approximate root. 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 , 0.156 ], [ 0.00 , 0.156 ] [ 0.00 , 1.00 ] Fritz John multipliers V: [ -1.00 , 1.00 ] INEQ_CERT_FEASIBLE: F F F F F F F T T T T T F F F NIN_POSS_BINDING: 10 Total volume of the boxes that have not yet been processed: 118979.58771839604