Output from FIND_GLOBAL_MIN on 05/07/2012 at 04:19:10. Version for the system is: March 13, 2009 Codelist file name is: ex14_2_8G.CDL Box data file name is: ex14_2_8.DT1 Initial box: [ 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 --------------------------------------- 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: [ 0.877 , 0.879 ], [ 0.121 , 0.123 ] [ 55.7 , 55.8 ], [ 0.00 , 0.150E-02 ] PHI: [ 0.00 , 0.150E-02 ] Box contains the following approximate root: 0.878 , 0.122 , 55.7 , -0.995E-08 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ -0.995E-08, -0.995E-08 ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.500 , 0.500 ] Fritz John multipliers U: [ 0.00 , 0.259 ], [ 0.00 , 0.256 ] [ 0.00 , 0.259 ], [ 0.00 , 0.256 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 0.814E-01 ], [ 0.00 , 0.814E-01 ] [ 0.00 , 0.507 ] Fritz John multipliers V: [ -0.178E-06, 0.178E-06 ] INEQ_CERT_FEASIBLE: F F F F T T T T T T F NIN_POSS_BINDING: 5 ------------------------------------------------- LIST OF BOXES CONTAINING VERIFIED FEASIBLE POINTS: Box no.: 1 Box coordinates: [ 0.499 , 0.501 ], [ 0.499 , 0.501 ] [ 57.3 , 57.4 ], [ 0.652E+04, 0.653E+04 ] PHI: [ 0.652E+04, 0.653E+04 ] Box contains the following approximate root: 0.500 , 0.500 , 57.4 , 0.652E+04 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 0.652E+04, 0.652E+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 ] Fritz John multipliers V: [ -1.00 , 1.00 ] INEQ_CERT_FEASIBLE: F F F F F F F F F F F NIN_POSS_BINDING: 11 ------------------------------------------------- ALGORITHM COULD NOT COMPLETE WITH LESS THAN 500000 BOXES CONSIDERED. Number of boxes that have not yet been processed: 5104 Number of bisections: 293038 No. dense interval residual evaluations -- gradient code list: 5690668 Number of orig. system inverse midpoint preconditioner rows: 5537331 Number of orig. system C-LP preconditioner rows: 2161305 Number of solutions for a component in the expanded system: 43946077 Total number of forward_substitutions: 16598759 Number of Gauss--Seidel steps on the dense system: 7708586 Number point dense residual evaluations, gradient codelist: 407171 Number of gradient evaluations from a gradient code list: 2045999 Total number of dense slope matrix evaluations: 4071740 Total number second-order interval evaluations of the original function: 717316 Total number dense interval constraint evaluations: 100679972 Total number dense interval constraint gradient component evaluations: 221562880 Total number dense point constraint gradient component evaluations: 26669952 Total number dense interval reduced gradient evaluations: 3450168 Total number of calls to FRITZ_JOHN_RESIDUALS: 886478 Number of times a box was rejected because the gradient or reduced gradient did not contain zero: 47872 Number of times a box was rejected due to infeasibility in LP_FILTER: 1248 Average number of overall loop iterations in each call to the reduced interval Newton method): 1.94 Number of times a box was rejected in the interval Newton method due to an empty intersection: 95793 Number of times the interval Newton method made a coordinate interval smaller: 717030 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 357774 Number of times a pivoting preconditioner was successful after the first sweep: 2526 Number of times a midpoint matrix was factored: 573224 Total number of times the reduced interval Newton method was tried: 479315 Number of times an inverse midpoint preconditioner led to improvement or rejection: 438709 Number of times a C LP preconditioner led to improvement or rejection: 16340 Number of times computing a C_LP failed 11 N_C_LP_INFEASIBLE = 278411 N_REJECT_WITH_LP filter = 1292 N_LPF_INF_OR_UNB = 278248 Number of possible splits as detected by the pivoting preconditioner: 838606 Total time spent in the LP filter (creating and solving the LP): 0.296E+04 Total time spent in subsit (constraint propagation): 43.1 Total time spent in reduced_interval_Newton (iteration to reduce the box): 644. Total time spent searching for "D" in the LP filter: 33.0 Total time spent actually solving the linear relaxations: 0.261E+04 Total time spent doing linear algebra (preconditioners and solution processes): 243. Total time spent running the approximate optimizer: 6.48 LIST_BOOKKEEPING_TIME: 140. FUNCTION_EVALUATION_TIME (in forward_substitution): 695. Time spent setting up pivoting preconditioners: 25.1 Time spent computing pivoting preconditioners: 30.6 Time spent computing LP preconditioners: 36.2 Time spent computing inverse midpoint preconditioners: 17.9 Number of times MAXIT was exceeded in C_LP_DENSE: 31 Number of unbounded problems found in C_LP_DENSE: 11 Number of times the approximate solver was called: 37226 Number Fritz-John matrix evaluations: 838606 Number of times SUBSIT decreased one or more coordinate widths: 627 Number of times SUBSIT rejected a box: 19392 Number times a box was rejected due infeasible inequality constraints: 79838 Total number of boxes processed in loop: 500000 N_FINDOPT_SUCCESS = 37225 BEST_ESTIMATE: 0.652E+04 Overall CPU time: 0.505E+04 CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 644. =================================================== =================================================== Number of boxes in the list with proven feasible points: 1 Number of boxes in the list of other small boxes: 1 Number of unfathomed boxes: 5104 Interval hull of the boxes verified to contain feasible points or critical points: [ 0.499 , 0.501 ], [ 0.499 , 0.501 ] [ 57.3 , 57.4 ], [ 0.652E+04, 0.653E+04 ] Interval hull of the small unverified boxes: [ 0.877 , 0.879 ], [ 0.121 , 0.123 ] [ 55.7 , 55.8 ], [ 0.00 , 0.150E-02 ] Interval hull of the unfathomed boxes: [ 0.100E-05, 1.00 ], [ 0.100E-05, 1.00 ] [ 40.0 , 90.0 ], [ 0.107E-01, 0.100E+05 ] Rigorously verified bounds on the optimum, provided an optimum exists: [ 0.00 , 0.652E+04 ] FIRST UNFINISHED BOX: Box coordinates: [ 0.878 , 0.879 ], [ 0.121 , 0.122 ] [ 55.4 , 55.5 ], [ 0.107E-01, 0.119E-01 ] PHI: [ 0.107E-01, 0.119E-01 ] Box does not contain an approximate root. Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.499 , 0.501 ] Fritz John multipliers U: [ 0.00 , 0.259 ], [ 0.00 , 0.256 ] [ 0.00 , 0.259 ], [ 0.00 , 0.256 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 0.814E-01 ], [ 0.00 , 0.814E-01 ] [ 0.00 , 0.936 ] Fritz John multipliers V: [ -0.235E-01, 0.235E-01 ] INEQ_CERT_FEASIBLE: F F F F T T T T T T T NIN_POSS_BINDING: 4 LAST UNFINISHED BOX: Box coordinates: [ 0.499 , 0.499 ], [ 0.501 , 0.501 ] [ 40.0 , 90.0 ], [ 0.500E+04, 0.100E+05 ] PHI: [ 0.500E+04, 0.100E+05 ] 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 , 0.922 ], [ 0.00 , 0.922 ] [ 0.00 , 0.922 ], [ 0.00 , 0.922 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 0.751E-01 ], [ 0.00 , 0.751E-01 ] [ 0.00 , 1.00 ] Fritz John multipliers V: [ -1.00 , 1.00 ] INEQ_CERT_FEASIBLE: F F F F T T T T F F F NIN_POSS_BINDING: 7 Total volume of the boxes that have not yet been processed: 248365.56275870750