Output from FIND_GLOBAL_MIN on 05/04/2012 at 19:44:05. Version for the system is: March 13, 2009 Codelist file name is: ex8_4_1G.CDL Box data file name is: ex8_4_1.DT1 Initial box: [ -0.500 , 0.500 ], [ 0.400 , 1.40 ] [ 1.30 , 2.30 ], [ 2.10 , 3.10 ] [ 2.80 , 3.80 ], [ 3.90 , 4.90 ] [ 4.70 , 5.70 ], [ 5.60 , 6.60 ] [ 6.00 , 7.00 ], [ 6.90 , 7.90 ] [ -2.00 , 2.00 ], [ 5.40 , 6.40 ] [ 4.90 , 5.90 ], [ 3.90 , 4.90 ] [ 4.10 , 5.10 ], [ 3.00 , 4.00 ] [ 3.20 , 4.20 ], [ 2.30 , 3.30 ] [ 2.30 , 3.30 ], [ 1.90 , 2.90 ] [ 1.00 , 2.00 ], [ 0.00 , 10.0 ] 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 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: [ -0.498E-01, -0.478E-01 ], [ 0.854 , 0.856 ] [ 1.97 , 1.97 ], [ 2.50 , 2.50 ] [ 3.50 , 3.51 ], [ 4.26 , 4.27 ] [ 5.26 , 5.27 ], [ 5.95 , 5.96 ] [ 6.43 , 6.44 ], [ 7.50 , 7.51 ] [ -0.547 , -0.545 ], [ 5.80 , 5.82 ] [ 5.31 , 5.32 ], [ 4.71 , 4.71 ] [ 4.41 , 4.42 ], [ 3.87 , 3.88 ] [ 3.45 , 3.46 ], [ 2.91 , 2.92 ] [ 2.53 , 2.54 ], [ 2.27 , 2.28 ] [ 1.69 , 1.69 ], [ 5.78 , 5.79 ] PHI: [ 0.596 , 0.642 ] Box contains the following approximate root: -0.488E-01, 0.855 , 1.97 , 2.50 , 3.50 , 4.27 5.26 , 5.96 , 6.43 , 7.50 , -0.546 , 5.81 5.32 , 4.71 , 4.42 , 3.87 , 3.46 , 2.91 2.53 , 2.28 , 1.69 , 5.78 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 0.619 , 0.619 ] 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 ] [ 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 ] 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 F F F F F F F F F F F F F F NIN_POSS_BINDING: 44 ------------------------------------------------- ALGORITHM COULD NOT COMPLETE IN 0.7200D+04 SECONDS OF CPU TIME. Number of boxes that have not yet been processed: 35672 Number of bisections: 36991 No. dense interval residual evaluations -- gradient code list: 583168 Number of orig. system inverse midpoint preconditioner rows: 5899055 Number of orig. system C-LP preconditioner rows: 1445863 Number of solutions for a component in the expanded system: 9833833 Total number of forward_substitutions: 4458926 Number of Gauss--Seidel steps on the dense system: 9503270 Number point dense residual evaluations, gradient codelist: 9 Number of gradient evaluations from a gradient code list: 189044 Total number of dense slope matrix evaluations: 2951278 Total number second-order interval evaluations of the original function: 74030 Total number dense interval constraint evaluations: 51064294 Total number dense interval constraint gradient component evaluations: 690899352 Total number dense point constraint gradient component evaluations: 11880 Total number dense interval reduced gradient evaluations: 523481 Total number of calls to FRITZ_JOHN_RESIDUALS: 130958 Number of times a box was rejected because of a large lower bound on the objective function: 1 Number of times a box was rejected because the gradient or reduced gradient did not contain zero: 174 Average number of overall loop iterations in each call to the reduced interval Newton method): 3.41 Number of times a box was rejected in the interval Newton method due to an empty intersection: 1188 Number of times the interval Newton method made a coordinate interval smaller: 462842 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 10170 Number of times a pivoting preconditioner was successful after the first sweep: 9062 Number of times a midpoint matrix was factored: 124942 Total number of times the reduced interval Newton method was tried: 38354 Number of times an inverse midpoint preconditioner led to improvement or rejection: 168490 Number of times a C LP preconditioner led to improvement or rejection: 285281 Number of times computing a C_LP failed 1043 N_C_LP_INFEASIBLE = 32885 N_LPF_INF_OR_UNB = 32885 Number of possible splits as detected by the pivoting preconditioner: 130781 Total time spent in the LP filter (creating and solving the LP): 344. Total time spent in subsit (constraint propagation): 5.35 Total time spent in reduced_interval_Newton (iteration to reduce the box): 0.665E+04 Total time spent searching for "D" in the LP filter: 40.4 Total time spent actually solving the linear relaxations: 267. Total time spent doing linear algebra (preconditioners and solution processes): 0.569E+04 LIST_BOOKKEEPING_TIME: 83.5 FUNCTION_EVALUATION_TIME (in forward_substitution): 71.4 Time spent setting up pivoting preconditioners: 76.1 Time spent computing pivoting preconditioners: 22.4 Time spent computing LP preconditioners: 0.241E+04 Time spent computing inverse midpoint preconditioners: 61.8 Number of times MAXIT was exceeded in C_LP_DENSE: 82957 Number of unbounded problems found in C_LP_DENSE: 1043 Number Fritz-John matrix evaluations: 130784 Number of times SUBSIT decreased one or more coordinate widths: 31508 Total number of boxes processed in loop: 38354 N_FINDOPT_SUCCESS = 1 BEST_ESTIMATE: 0.619 Overall CPU time: 0.720E+04 CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 0.665E+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: 35672 Interval hull of the boxes verified to contain feasible points or critical points: [ -0.498E-01, -0.478E-01 ], [ 0.854 , 0.856 ] [ 1.97 , 1.97 ], [ 2.50 , 2.50 ] [ 3.50 , 3.51 ], [ 4.26 , 4.27 ] [ 5.26 , 5.27 ], [ 5.95 , 5.96 ] [ 6.43 , 6.44 ], [ 7.50 , 7.51 ] [ -0.547 , -0.545 ], [ 5.80 , 5.82 ] [ 5.31 , 5.32 ], [ 4.71 , 4.71 ] [ 4.41 , 4.42 ], [ 3.87 , 3.88 ] [ 3.45 , 3.46 ], [ 2.91 , 2.92 ] [ 2.53 , 2.54 ], [ 2.27 , 2.28 ] [ 1.69 , 1.69 ], [ 5.78 , 5.79 ] Interval hull of the unfathomed boxes: [ -0.500 , 0.500 ], [ 0.400 , 1.40 ] [ 1.30 , 2.30 ], [ 2.10 , 3.10 ] [ 2.80 , 3.80 ], [ 3.90 , 4.90 ] [ 4.70 , 5.70 ], [ 5.60 , 6.60 ] [ 6.00 , 7.00 ], [ 6.90 , 7.90 ] [ -2.00 , 2.00 ], [ 5.40 , 6.40 ] [ 4.90 , 5.90 ], [ 3.90 , 4.90 ] [ 4.10 , 5.10 ], [ 3.00 , 4.00 ] [ 3.20 , 4.20 ], [ 2.30 , 3.30 ] [ 2.30 , 3.30 ], [ 1.90 , 2.90 ] [ 1.00 , 2.00 ], [ 0.00 , 10.0 ] Rigorously verified bounds on the optimum, provided an optimum exists: [ 0.596 , 0.619 ] FIRST UNFINISHED BOX: Box coordinates: [ -0.500 , -0.498E-01 ], [ 0.900 , 1.40 ] [ 1.80 , 2.30 ], [ 2.10 , 2.60 ] [ 3.30 , 3.80 ], [ 3.90 , 4.28 ] [ 5.20 , 5.70 ], [ 5.60 , 6.03 ] [ 6.25 , 6.50 ], [ 7.42 , 7.90 ] [ -0.599 , -0.577 ], [ 5.80 , 6.19 ] [ 4.93 , 5.37 ], [ 4.40 , 4.85 ] [ 4.22 , 4.68 ], [ 3.50 , 3.99 ] [ 3.42 , 3.64 ], [ 2.36 , 2.89 ] [ 2.30 , 2.66 ], [ 1.90 , 2.23 ] [ 1.04 , 1.50 ], [ 5.77 , 5.89 ] PHI: [ 0.747E-01, 4.19 ] 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 , 0.948E-01 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 0.171 ] [ 0.00 , 1.00 ], [ 0.00 , 0.105 ] [ 0.00 , 0.110 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 0.125 ] [ 0.00 , 0.249 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 0.241 ] [ 0.00 , 0.725 ], [ 0.00 , 1.00 ] [ 0.00 , 0.599 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 0.285 ] [ 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: [ -0.338 , 0.331 ], [ -0.486 , 0.433 ] [ -0.366 , 0.905 ], [ -0.785 , 0.375 ] [ -0.403 , 0.962 ], [ -0.559 , 0.221 ] [ -0.440 , 0.508 ], [ -1.00 , 0.325 ] [ -1.00 , 0.329 ], [ -0.465 , 0.500 ] INEQ_CERT_FEASIBLE: F T T F T F F T T F F T T F F T F T T F T T T T T T T T T T T T T T T T F T F T T T T T NIN_POSS_BINDING: 12 LAST UNFINISHED BOX: Box coordinates: [ -0.498E-01, -0.478E-01 ], [ 0.854 , 0.856 ] [ 1.97 , 1.97 ], [ 2.50 , 2.50 ] [ 3.50 , 3.51 ], [ 4.26 , 4.27 ] [ 5.26 , 5.27 ], [ 5.95 , 5.96 ] [ 6.43 , 6.44 ], [ 7.50 , 7.51 ] [ -0.547 , -0.545 ], [ 5.80 , 5.82 ] [ 5.31 , 5.32 ], [ 4.71 , 4.71 ] [ 4.41 , 4.42 ], [ 3.87 , 3.88 ] [ 3.45 , 3.46 ], [ 2.91 , 2.92 ] [ 2.53 , 2.54 ], [ 2.27 , 2.28 ] [ 1.69 , 2.00 ], [ 0.00 , 10.0 ] PHI: [ 0.597 , 0.855 ] Box contains the following approximate root: -0.488E-01, 0.855 , 1.97 , 2.50 , 3.50 , 4.27 5.26 , 5.96 , 6.43 , 7.50 , -0.546 , 5.81 5.32 , 4.71 , 4.42 , 3.87 , 3.46 , 2.91 2.53 , 2.28 , 1.85 , 5.00 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 0.702 , 0.702 ] 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 ] [ 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 ] 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 F F F F F F F F F F F F F F NIN_POSS_BINDING: 44 Total volume of the boxes that have not yet been processed: 1.90474236318043279E-004