Output from FIND_GLOBAL_MIN on 05/07/2012 at 13:43:58. Version for the system is: March 13, 2009 Codelist file name is: himmel11G.CDL Box data file name is: himmel11.DT1 Initial box: [ 78.0 , 102. ], [ 27.0 , 45.0 ] [ 27.0 , 45.0 ], [ 33.0 , 45.0 ] [ 27.0 , 45.0 ], [ 0.00 , 92.0 ] [ 90.0 , 110. ], [ 20.0 , 25.0 ] [ 0.00 , 0.100E+05 ] BOUND_CONSTRAINT: 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. LIST OF SMALL BOXES: Box no.: 1 Box coordinates: [ 78.0 , 78.1 ], [ 30.0 , 30.0 ] [ 36.7 , 36.8 ], [ 33.0 , 33.0 ] [ 44.9 , 45.0 ], [ 91.9 , 92.0 ] [ 98.7 , 98.9 ], [ 20.0 , 20.0 ] [ 0.00 , 0.150E-02 ] PHI: [ -0.307E+05, -0.306E+05 ] Box contains the following approximate root: 78.0 , 30.0 , 36.8 , 33.0 , 45.0 , 92.0 98.8 , 20.0 , -0.100E-07 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ -0.307E+05, -0.307E+05 ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.112E-03, 0.112E-03 ] Fritz John multipliers U: [ 0.00 , 1.00 ], [ 0.550E-02, 0.550E-02 ] [ 0.00 , 0.277 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 0.478 ] [ 0.00 , 0.188E-01 ], [ 0.948E-02, 0.948E-02 ] [ 0.00 , 0.138E-26 ], [ 0.00 , 0.679E-20 ] [ 0.299E-02, 0.299E-02 ], [ 0.00 , 1.00 ] [ 0.453E-01, 0.453E-01 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.910E-01, 0.910E-01 ] [ 0.00 , 1.00 ], [ 0.835 , 0.835 ] Fritz John multipliers V: [ -0.453E-01, -0.453E-01 ], [ -0.355E-29, 0.355E-29 ] [ 0.910E-01, 0.910E-01 ] INEQ_CERT_FEASIBLE: T F T T T T T F F F F T F T T F T F NIN_POSS_BINDING: 8 ------------------------------------------------- THERE WERE NO BOXES CORRESPONDING TO VERIFIED FEASIBLE POINTS. ALGORITHM COMPLETED WITH LESS THAN THE MAXIMUM NUMBER, 500000 OF BOXES. Number of bisections: 695 No. dense interval residual evaluations -- gradient code list: 23356 Number of orig. system inverse midpoint preconditioner rows: 151797 Number of orig. system C-LP preconditioner rows: 10519 Number of solutions for a component in the expanded system: 122812 Total number of forward_substitutions: 86139 Number of Gauss--Seidel steps on the dense system: 201475 Number point dense residual evaluations, gradient codelist: 35 Number of gradient evaluations from a gradient code list: 5557 Total number of dense slope matrix evaluations: 95068 Total number second-order interval evaluations of the original function: 1405 Total number dense interval constraint evaluations: 1133337 Total number dense interval constraint gradient component evaluations: 7028910 Total number dense point constraint gradient component evaluations: 82593 Total number dense interval reduced gradient evaluations: 42452 Total number of calls to FRITZ_JOHN_RESIDUALS: 10819 Number of times a box was rejected because the gradient or reduced gradient did not contain zero: 411 Average number of overall loop iterations in each call to the reduced interval Newton method): 7.79 Number of times a box was rejected in the interval Newton method due to an empty intersection: 281 Number of times the interval Newton method made a coordinate interval smaller: 27397 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 4211 Number of times a pivoting preconditioner was successful after the first sweep: 2718 Number of times a midpoint matrix was factored: 7313 Total number of times the reduced interval Newton method was tried: 1388 Number of times an inverse midpoint preconditioner led to improvement or rejection: 18735 Number of times a C LP preconditioner led to improvement or rejection: 4732 N_C_LP_INFEASIBLE = 13 N_LPF_INF_OR_UNB = 13 Number of possible splits as detected by the pivoting preconditioner: 10407 Total time spent in the LP filter (creating and solving the LP): 8.25 Total time spent in subsit (constraint propagation): 0.840E-01 Total time spent in reduced_interval_Newton (iteration to reduce the box): 24.4 Total time spent searching for "D" in the LP filter: 1.78 Total time spent actually solving the linear relaxations: 5.33 Total time spent doing linear algebra (preconditioners and solution processes): 19.0 Total time spent running the approximate optimizer: 0.800E-02 LIST_BOOKKEEPING_TIME: 0.520E-01 FUNCTION_EVALUATION_TIME (in forward_substitution): 0.788 Time spent setting up pivoting preconditioners: 1.12 Time spent computing pivoting preconditioners: 0.856 Time spent computing LP preconditioners: 2.06 Time spent computing inverse midpoint preconditioners: 0.672 Number of times MAXIT was exceeded in C_LP_DENSE: 99 Number of times the approximate solver was called: 2 Number Fritz-John matrix evaluations: 10407 Number of times SUBSIT decreased one or more coordinate widths: 1261 Number of times SUBSIT rejected a box: 3 Number times a box was rejected due infeasible inequality constraints: 2 Total number of boxes processed in loop: 1391 BEST_ESTIMATE: 0.500E+08 Overall CPU time: 33.6 CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 24.4 =================================================== =================================================== Number of boxes in the list with proven feasible points: 0 Number of boxes in the list of other small boxes: 1 Number of unfathomed boxes: 0 Interval hull of the small unverified boxes: [ 78.0 , 78.1 ], [ 30.0 , 30.0 ] [ 36.7 , 36.8 ], [ 33.0 , 33.0 ] [ 44.9 , 45.0 ], [ 91.9 , 92.0 ] [ 98.7 , 98.9 ], [ 20.0 , 20.0 ] [ 0.00 , 0.150E-02 ] Rigorously verified bounds on the optimum, provided an optimum exists: [ -0.307E+05, -0.306E+05 ]