Output from FIND_GLOBAL_MIN on 05/06/2012 at 22:14:58. Version for the system is: March 13, 2009 Codelist file name is: houseG.CDL Box data file name is: house.DT1 Initial box: [ -0.100E+05, 0.100E+05 ], [ -0.100E+05, 0.100E+05 ] [ -0.100E+05, 0.100E+05 ], [ 40.0 , 68.0 ] [ -0.100E+05, 0.100E+05 ], [ 56.0 , 100. ] [ -0.100E+05, 0.300E+04 ], [ -0.100E+05, 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: [ 25.8 , 25.8 ], [ 58.0 , 58.2 ] [ 58.0 , 58.2 ], [ 51.6 , 51.7 ] [ 29.0 , 29.1 ], [ 87.1 , 87.2 ] [ 0.300E+04, 0.300E+04 ], [ 0.150E+04, 0.150E+04 ] PHI: [ -0.450E+04, -0.449E+04 ] Box contains the following approximate root: 34.0 , 44.1 , 44.1 , 68.0 , 22.1 , 66.2 0.300E+04, 0.150E+04 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ -0.450E+04, -0.450E+04 ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.211E-01, 0.328E-01 ] Fritz John multipliers U: [ 0.00 , 0.112E-01 ], [ 0.00 , 1.00 ] [ 0.165 , 0.662 ], [ 0.00 , 0.299 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 0.283 ] [ 0.318E-01, 0.546E-01 ] Fritz John multipliers V: [ -0.222E-01, -0.104E-01 ], [ 0.211E-01, 0.328E-01 ] [ -0.690E-30, 0.789E-30 ], [ 0.548 , 0.844 ] INEQ_CERT_FEASIBLE: F T F T T T T T F NIN_POSS_BINDING: 3 ------------------------------------------------- Box no.: 2 Box coordinates: [ 23.1 , 23.1 ], [ 64.9 , 65.0 ] [ 64.9 , 65.0 ], [ 46.1 , 46.2 ] [ 32.5 , 32.5 ], [ 97.4 , 97.6 ] [ 0.300E+04, 0.300E+04 ], [ 0.150E+04, 0.150E+04 ] PHI: [ -0.450E+04, -0.449E+04 ] Box contains the following approximate root: 34.0 , 44.1 , 44.1 , 68.0 , 22.1 , 66.2 0.300E+04, 0.150E+04 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ -0.450E+04, -0.450E+04 ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.205E-01, 0.371E-01 ] Fritz John multipliers U: [ 0.00 , 0.124E-01 ], [ 0.00 , 1.00 ] [ 0.00 , 0.768 ], [ 0.00 , 0.293 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 0.437 ] [ 0.307E-01, 0.618E-01 ] Fritz John multipliers V: [ -0.247E-01, -0.102E-01 ], [ 0.205E-01, 0.371E-01 ] [ -0.136E-29, 0.155E-29 ], [ 0.471 , 0.856 ] INEQ_CERT_FEASIBLE: F T F F T T T T F NIN_POSS_BINDING: 4 ------------------------------------------------- THERE WERE NO BOXES CORRESPONDING TO VERIFIED FEASIBLE POINTS. ALGORITHM COULD NOT COMPLETE IN 0.7200D+04 SECONDS OF CPU TIME. Number of boxes that have not yet been processed: 168392 Number of bisections: 265828 No. dense interval residual evaluations -- gradient code list: 5479390 Number of orig. system inverse midpoint preconditioner rows: 18444014 Number of orig. system C-LP preconditioner rows: 1294074 Number of solutions for a component in the expanded system: 24121255 Total number of forward_substitutions: 23714882 Number of Gauss--Seidel steps on the dense system: 21502139 Number point dense residual evaluations, gradient codelist: 160 Number of gradient evaluations from a gradient code list: 1468771 Total number of dense slope matrix evaluations: 14254974 Total number second-order interval evaluations of the original function: 702950 Total number dense interval constraint evaluations: 126285883 Total number dense interval constraint gradient component evaluations: 683386808 Total number dense point constraint gradient component evaluations: 118664 Total number dense interval reduced gradient evaluations: 6816506 Total number of calls to FRITZ_JOHN_RESIDUALS: 1714250 Number of times a box was rejected because the constraints were not satisfied: 144 Number of times a box was rejected because the gradient or reduced gradient did not contain zero: 20246 Number of times a box was rejected due to infeasibility in LP_FILTER: 2 Average number of overall loop iterations in each call to the reduced interval Newton method): 5.93 Number of times a box was rejected in the interval Newton method due to an empty intersection: 2535 Number of times the interval Newton method made a coordinate interval smaller: 2630102 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 790355 Number of times a pivoting preconditioner was successful after the first sweep: 466254 Number of times a midpoint matrix was factored: 1170569 Total number of times the reduced interval Newton method was tried: 289134 Number of times an inverse midpoint preconditioner led to improvement or rejection: 1535120 Number of times a C LP preconditioner led to improvement or rejection: 307162 Number of times computing a C_LP failed 2785 N_C_LP_INFEASIBLE = 46547 N_REJECT_WITH_LP filter = 2 N_LPF_INF_OR_UNB = 46546 Number of possible splits as detected by the pivoting preconditioner: 1694003 Total time spent in the LP filter (creating and solving the LP): 876. Total time spent in subsit (constraint propagation): 15.1 Total time spent in reduced_interval_Newton (iteration to reduce the box): 0.185E+04 Total time spent actually solving the linear relaxations: 811. Total time spent doing linear algebra (preconditioners and solution processes): 0.135E+04 Total time spent running the approximate optimizer: 0.280E-01 LIST_BOOKKEEPING_TIME: 0.450E+04 FUNCTION_EVALUATION_TIME (in forward_substitution): 113. Time spent setting up pivoting preconditioners: 159. Time spent computing pivoting preconditioners: 99.2 Time spent computing LP preconditioners: 127. Time spent computing inverse midpoint preconditioners: 68.5 Number of times MAXIT was exceeded in C_LP_DENSE: 1640 Number of unbounded problems found in C_LP_DENSE: 2785 Number of times the approximate solver was called: 5 Number Fritz-John matrix evaluations: 1694003 Number of times SUBSIT decreased one or more coordinate widths: 236671 Number of times SUBSIT rejected a box: 5244 Number times a box was rejected due infeasible inequality constraints: 21873 Total number of boxes processed in loop: 315869 BEST_ESTIMATE: 0.200E+05 Overall CPU time: 0.739E+04 CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 0.185E+04 =================================================== =================================================== Number of boxes in the list with proven feasible points: 0 Number of boxes in the list of other small boxes: 2 Number of unfathomed boxes: 168392 Interval hull of the small unverified boxes: [ 23.1 , 25.8 ], [ 58.0 , 65.0 ] [ 58.0 , 65.0 ], [ 46.1 , 51.7 ] [ 29.0 , 32.5 ], [ 87.1 , 97.6 ] [ 0.300E+04, 0.300E+04 ], [ 0.150E+04, 0.150E+04 ] Interval hull of the unfathomed boxes: [ 13.3 , 34.0 ], [ 27.4 , 79.6 ] [ 34.9 , 81.1 ], [ 40.0 , 68.0 ] [ 13.7 , 62.1 ], [ 56.0 , 100. ] [ 915. , 0.300E+04 ], [ 465. , 0.165E+04 ] Rigorously verified bounds on the optimum, provided an optimum exists: [ -0.450E+04, -0.138E+04 ] FIRST UNFINISHED BOX: Box coordinates: [ 31.4 , 31.4 ], [ 47.8 , 47.8 ] [ 47.8 , 47.8 ], [ 62.7 , 62.7 ] [ 23.9 , 23.9 ], [ 71.7 , 71.7 ] [ 0.300E+04, 0.300E+04 ], [ 0.150E+04, 0.150E+04 ] PHI: [ -0.450E+04, -0.450E+04 ] Box does not contain an approximate root. Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.210E-01, 0.262E-01 ] Fritz John multipliers U: [ 0.00 , 0.893E-02 ], [ 0.00 , 1.00 ] [ 0.00 , 0.529 ], [ 0.00 , 0.289 ] [ 0.00 , 1.00 ], [ 0.00 , 0.506 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.316E-01, 0.438E-01 ] Fritz John multipliers V: [ -0.176E-01, -0.103E-01 ], [ 0.210E-01, 0.262E-01 ] [ -0.214E-29, 0.254E-29 ], [ 0.659 , 0.824 ] INEQ_CERT_FEASIBLE: F T F F T T T T F NIN_POSS_BINDING: 4 LAST UNFINISHED BOX: Box coordinates: [ 13.3 , 23.7 ], [ 53.5 , 79.6 ] [ 34.9 , 69.9 ], [ 40.0 , 68.0 ] [ 13.7 , 39.8 ], [ 56.0 , 100. ] [ 915. , 0.196E+04 ], [ 465. , 0.165E+04 ] PHI: [ -0.361E+04, -0.138E+04 ] Box does not contain an approximate root. Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.00 , 0.500E-01 ] Fritz John multipliers U: [ 0.00 , 0.564E-01 ], [ 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 , 0.150 ] Fritz John multipliers V: [ -0.309E-15, 0.500E-01 ], [ -0.999E-15, 0.500E-01 ] [ -1.00 , 1.00 ], [ -0.258 , 0.877 ] INEQ_CERT_FEASIBLE: F F F F F F F F T NIN_POSS_BINDING: 8 Total volume of the boxes that have not yet been processed: 1059936415894737.4