Output from FIND_GLOBAL_MIN on 05/08/2012 at 00:32:34. Version for the system is: March 13, 2009 Codelist file name is: ex8_4_5_sourceG.CDL Box data file name is: ex8_4_5_source.DT1 Initial box: [ -0.289 , 0.289 ], [ -0.289 , 0.289 ] [ -0.289 , 0.289 ], [ -0.289 , 0.289 ] [ 0.176 , 0.216 ], [ 0.175 , 0.215 ] [ 0.153 , 0.194 ], [ 0.140 , 0.180 ] [ 0.644E-01, 0.104 ], [ 0.427E-01, 0.827E-01 ] [ 0.256E-01, 0.656E-01 ], [ 0.142E-01, 0.542E-01 ] [ 0.123E-01, 0.523E-01 ], [ 0.350E-02, 0.435E-01 ] [ 0.460E-02, 0.446E-01 ] BOUND_CONSTRAINT: F F F F F F F F F F F F F F F F 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. THERE WERE NO BOXES IN THE LIST OF SMALL BOXES. LIST OF BOXES CONTAINING VERIFIED FEASIBLE POINTS: Box no.: 1 Box coordinates: [ 0.192 , 0.194 ], [ 0.190 , 0.192 ] [ 0.122 , 0.124 ], [ 0.135 , 0.137 ] [ 0.193 , 0.195 ], [ 0.192 , 0.194 ] [ 0.181 , 0.183 ], [ 0.148 , 0.150 ] [ 0.918E-01, 0.938E-01 ], [ 0.614E-01, 0.634E-01 ] [ 0.446E-01, 0.466E-01 ], [ 0.345E-01, 0.365E-01 ] [ 0.278E-01, 0.298E-01 ], [ 0.231E-01, 0.251E-01 ] [ 0.197E-01, 0.217E-01 ] PHI: [ 0.235E-03, 0.401E-03 ] Box contains the following approximate root: 0.193 , 0.191 , 0.123 , 0.136 , 0.194 , 0.193 0.182 , 0.149 , 0.928E-01, 0.624E-01, 0.456E-01, 0.355E-01 0.288E-01, 0.241E-01, 0.207E-01 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 0.307E-03, 0.307E-03 ] 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 ], [ 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 ], [ -1.00 , 1.00 ] [ -1.00 , 1.00 ], [ -1.00 , 1.00 ] [ -1.00 , 1.00 ], [ -1.00 , 1.00 ] [ -1.00 , 1.00 ], [ -1.00 , 1.00 ] [ -1.00 , 1.00 ], [ -1.00 , 1.00 ] [ -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 F F F F F F F F F F F NIN_POSS_BINDING: 30 ------------------------------------------------- ALGORITHM COMPLETED WITH LESS THAN THE MAXIMUM NUMBER, 500000 OF BOXES. Number of bisections: 9495 No. dense interval residual evaluations -- gradient code list: 256283 Number of orig. system inverse midpoint preconditioner rows: 1167920 Number of orig. system C-LP preconditioner rows: 108649 Number of solutions for a component in the expanded system: 3650268 Total number of forward_substitutions: 1280884 Number of Gauss--Seidel steps on the dense system: 1349175 Number point dense residual evaluations, gradient codelist: 6669 Number of gradient evaluations from a gradient code list: 68335 Total number of dense slope matrix evaluations: 1507438 Total number second-order interval evaluations of the original function: 21568 Total number dense interval constraint evaluations: 16044341 Total number dense interval constraint gradient component evaluations: 141517530 Total number dense point constraint gradient component evaluations: 4129110 Total number dense interval reduced gradient evaluations: 394943 Total number of calls to FRITZ_JOHN_RESIDUALS: 99171 Number of times a box was rejected because of a large lower bound on the objective function: 871 Number of times a box was rejected because the constraints were not satisfied: 1788 Number of times a box was rejected because the gradient or reduced gradient did not contain zero: 113 Number of times feasible point was found based on the LP_FILTER approximate solution: 7 Number of times a box was rejected due to large lower bound on objective from LP_FILTER 9 Average number of overall loop iterations in each call to the reduced interval Newton method): 6.15 Number of times a box was rejected in the interval Newton method due to an empty intersection: 4049 Number of times the interval Newton method made a coordinate interval smaller: 578642 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 217807 Number of times a pivoting preconditioner was successful after the first sweep: 109704 Number of times a midpoint matrix was factored: 46936 Total number of times the reduced interval Newton method was tried: 16316 Number of times an inverse midpoint preconditioner led to improvement or rejection: 285715 Number of times a C LP preconditioner led to improvement or rejection: 38264 Number of times computing a C_LP failed 5199 N_C_LP_INFEASIBLE = 13555 N_NEW_BEST_ESTIMATE_WITH_LP filter = 7 N_REJECT_WITH_LP filter = 1 N_LPF_INF_OR_UNB = 13545 Number of possible splits as detected by the pivoting preconditioner: 97543 Total time spent in the LP filter (creating and solving the LP): 285. Total time spent in subsit (constraint propagation): 2.42 Total time spent in reduced_interval_Newton (iteration to reduce the box): 392. Total time spent searching for "D" in the LP filter: 1.67 Total time spent actually solving the linear relaxations: 266. Total time spent doing linear algebra (preconditioners and solution processes): 226. LIST_BOOKKEEPING_TIME: 2.69 FUNCTION_EVALUATION_TIME (in forward_substitution): 29.7 Time spent setting up pivoting preconditioners: 24.4 Time spent computing pivoting preconditioners: 11.9 Time spent computing LP preconditioners: 29.4 Time spent computing inverse midpoint preconditioners: 10.8 Number of times MAXIT was exceeded in C_LP_DENSE: 1188 Number of unbounded problems found in C_LP_DENSE: 5199 Number Fritz-John matrix evaluations: 99058 Number of times SUBSIT decreased one or more coordinate widths: 9028 Number of times SUBSIT rejected a box: 363 Total number of boxes processed in loop: 16696 N_FINDOPT_SUCCESS = 505 BEST_ESTIMATE: 0.307E-03 Overall CPU time: 758. CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 392. =================================================== =================================================== 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: 0 Interval hull of the boxes verified to contain feasible points or critical points: [ 0.192 , 0.194 ], [ 0.190 , 0.192 ] [ 0.122 , 0.124 ], [ 0.135 , 0.137 ] [ 0.193 , 0.195 ], [ 0.192 , 0.194 ] [ 0.181 , 0.183 ], [ 0.148 , 0.150 ] [ 0.918E-01, 0.938E-01 ], [ 0.614E-01, 0.634E-01 ] [ 0.446E-01, 0.466E-01 ], [ 0.345E-01, 0.365E-01 ] [ 0.278E-01, 0.298E-01 ], [ 0.231E-01, 0.251E-01 ] [ 0.197E-01, 0.217E-01 ] Rigorously verified bounds on the optimum, provided an optimum exists: [ 0.235E-03, 0.307E-03 ]