Output from FIND_GLOBAL_MIN on 05/08/2012 at 00:25:09. Version for the system is: March 13, 2009 Codelist file name is: ex6_1_1G.CDL Box data file name is: ex6_1_1.DT1 Initial box: [ 0.100E-06, 0.500 ], [ 0.100E-06, 0.500 ] [ 0.100E-06, 0.500 ], [ 0.100E-06, 0.500 ] [ 0.00 , 0.100E+05 ], [ 0.00 , 0.100E+05 ] [ 0.00 , 0.100E+05 ], [ 0.00 , 0.100E+05 ] BOUND_CONSTRAINT: 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. LIST OF SMALL BOXES: Box no.: 1 Box coordinates: [ 0.498 , 0.500 ], [ 0.100E-06, 0.186E-02 ] [ 0.343 , 0.345 ], [ 0.155 , 0.157 ] [ 0.900 , 0.902 ], [ 0.270E-01, 0.290E-01 ] [ 0.690 , 0.692 ], [ 0.998 , 1.00 ] PHI: [ -0.541E-01, -0.524E-02 ] Box contains the following approximate root: 0.234 , 0.266 , 0.234 , 0.266 , 0.863 , 0.863 0.765 , 0.765 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ -0.176E-01, -0.176E-01 ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.192 , 0.192 ] 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 , 0.521 ] [ 0.00 , 1.00 ], [ 0.00 , 0.557 ] Fritz John multipliers V: [ -0.891E-01, -0.891E-01 ], [ -0.876 , -0.876 ] [ -0.178 , -0.178 ], [ -0.813E-03, -0.813E-03 ] [ 0.700E-02, 0.700E-02 ], [ 0.765E-03, 0.765E-03 ] INEQ_CERT_FEASIBLE: T T T T T T T T T T T T NIN_POSS_BINDING: 0 ------------------------------------------------- LIST OF BOXES CONTAINING VERIFIED FEASIBLE POINTS: Box no.: 1 Box coordinates: [ 0.497 , 0.499 ], [ 0.113E-02, 0.313E-02 ] [ 0.335E-01, 0.355E-01 ], [ 0.464 , 0.466 ] [ 0.988 , 0.990 ], [ 0.270E-01, 0.290E-01 ] [ 0.183 , 0.185 ], [ 0.998 , 1.00 ] PHI: [ -0.395E-01, -0.134E-02 ] Box contains the following approximate root: 0.498 , 0.213E-02, 0.345E-01, 0.465 , 0.989 , 0.280E-01 0.184 , 0.999 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ -0.196E-01, -0.196E-01 ] 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 ] 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 ] INEQ_CERT_FEASIBLE: F F F F F F F F F F F F NIN_POSS_BINDING: 12 ------------------------------------------------- Box no.: 2 Box coordinates: [ 0.100E-06, 0.171E-02 ], [ 0.498 , 0.500 ] [ 0.155 , 0.157 ], [ 0.343 , 0.345 ] [ 0.270E-01, 0.290E-01 ], [ 0.900 , 0.902 ] [ 0.998 , 1.00 ], [ 0.690 , 0.692 ] PHI: [ -0.516E-01, -0.559E-02 ] Box contains the following approximate root: 0.857E-03, 0.499 , 0.156 , 0.344 , 0.280E-01, 0.901 0.999 , 0.691 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ -0.208E-01, -0.208E-01 ] 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 ] 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 ] INEQ_CERT_FEASIBLE: F F F F F F F F F F F F NIN_POSS_BINDING: 12 ------------------------------------------------- ALGORITHM COMPLETED WITH LESS THAN THE MAXIMUM NUMBER, 500000 OF BOXES. Number of bisections: 18169 No. dense interval residual evaluations -- gradient code list: 442072 Number of orig. system inverse midpoint preconditioner rows: 996634 Number of orig. system C-LP preconditioner rows: 174360 Number of solutions for a component in the expanded system: 885740 Total number of forward_substitutions: 2081122 Number of Gauss--Seidel steps on the dense system: 1395659 Number point dense residual evaluations, gradient codelist: 19830 Number of gradient evaluations from a gradient code list: 112789 Total number of dense slope matrix evaluations: 1353674 Total number second-order interval evaluations of the original function: 63290 Total number dense interval constraint evaluations: 11546502 Total number dense interval constraint gradient component evaluations: 56934816 Total number dense point constraint gradient component evaluations: 2515968 Total number dense interval reduced gradient evaluations: 644422 Total number of calls to FRITZ_JOHN_RESIDUALS: 162425 Number of times a box was rejected because of a large lower bound on the objective function: 31 Number of times a box was rejected because the constraints were not satisfied: 5 Number of times a box was rejected because the gradient or reduced gradient did not contain zero: 1126 Number of times feasible point was found based on the LP_FILTER approximate solution: 5 Average number of overall loop iterations in each call to the reduced interval Newton method): 6.27 Number of times a box was rejected in the interval Newton method due to an empty intersection: 6100 Number of times the interval Newton method made a coordinate interval smaller: 410181 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 206134 Number of times a pivoting preconditioner was successful after the first sweep: 111655 Number of times a midpoint matrix was factored: 69568 Total number of times the reduced interval Newton method was tried: 25432 Number of times an inverse midpoint preconditioner led to improvement or rejection: 90298 Number of times a C LP preconditioner led to improvement or rejection: 95572 Number of times computing a C_LP failed 2925 N_C_LP_INFEASIBLE = 2331 N_NEW_BEST_ESTIMATE_WITH_LP filter = 5 N_LPF_INF_OR_UNB = 2331 Number of possible splits as detected by the pivoting preconditioner: 158274 Total time spent in the LP filter (creating and solving the LP): 124. Total time spent in subsit (constraint propagation): 1.97 Total time spent in reduced_interval_Newton (iteration to reduce the box): 162. Total time spent searching for "D" in the LP filter: 0.768 Total time spent actually solving the linear relaxations: 107. Total time spent doing linear algebra (preconditioners and solution processes): 81.0 Total time spent running the approximate optimizer: 0.280E-01 LIST_BOOKKEEPING_TIME: 12.0 FUNCTION_EVALUATION_TIME (in forward_substitution): 101. Time spent setting up pivoting preconditioners: 11.0 Time spent computing pivoting preconditioners: 8.76 Time spent computing LP preconditioners: 10.4 Time spent computing inverse midpoint preconditioners: 3.44 Number of times MAXIT was exceeded in C_LP_DENSE: 4076 Number of unbounded problems found in C_LP_DENSE: 2996 Number of times the approximate solver was called: 978 Number Fritz-John matrix evaluations: 161298 Number of times SUBSIT decreased one or more coordinate widths: 1264 Number of times SUBSIT rejected a box: 145 Total number of boxes processed in loop: 25582 N_FINDOPT_SUCCESS = 1007 BEST_ESTIMATE: -0.202E-01 Overall CPU time: 445. CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 162. =================================================== =================================================== Number of boxes in the list with proven feasible points: 2 Number of boxes in the list of other small boxes: 1 Number of unfathomed boxes: 0 Interval hull of the boxes verified to contain feasible points or critical points: [ 0.100E-06, 0.499 ], [ 0.113E-02, 0.500 ] [ 0.335E-01, 0.157 ], [ 0.343 , 0.466 ] [ 0.270E-01, 0.990 ], [ 0.270E-01, 0.902 ] [ 0.183 , 1.00 ], [ 0.690 , 1.00 ] Interval hull of the small unverified boxes: [ 0.498 , 0.500 ], [ 0.100E-06, 0.186E-02 ] [ 0.343 , 0.345 ], [ 0.155 , 0.157 ] [ 0.900 , 0.902 ], [ 0.270E-01, 0.290E-01 ] [ 0.690 , 0.692 ], [ 0.998 , 1.00 ] Rigorously verified bounds on the optimum, provided an optimum exists: [ -0.541E-01, -0.202E-01 ]