Output from FIND_GLOBAL_MIN on 05/04/2012 at 17:44:00. Version for the system is: March 13, 2009 Codelist file name is: haverlyG.CDL Box data file name is: haverly.DT1 Initial box: [ 0.00 , 0.100E+05 ], [ 0.00 , 0.100E+05 ] [ 0.00 , 0.100E+05 ], [ 0.00 , 0.100E+05 ] [ 0.00 , 0.100E+05 ], [ 0.00 , 0.100E+05 ] [ 0.00 , 0.100E+05 ], [ 0.00 , 0.100E+05 ] [ 0.00 , 100. ], [ 0.00 , 200. ] [ 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 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: [ 0.00 , 0.150E-02 ], [ 99.9 , 100. ] [ 0.999 , 1.00 ], [ 0.260E+04, 0.260E+04 ] [ 0.300E+04, 0.300E+04 ], [ 0.00 , 0.150E-02 ] [ 99.9 , 100. ], [ 99.9 , 100. ] [ 0.00 , 0.150E-02 ], [ 200. , 200. ] [ 0.00 , 0.150E-02 ], [ 99.9 , 100. ] PHI: [ -406. , -394. ] Box contains the following approximate root: -0.100E-07, 100. , 1.00 , 0.260E+04, 0.300E+04, -0.100E-07 100. , 100. , 0.457E-11, 200. , 0.100E-07, 100. OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ -400. , -400. ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.245E-01, 0.255E-01 ] Fritz John multipliers U: [ 0.00 , 0.532E-01 ], [ 0.147 , 0.153 ] [ 0.997E-01, 0.183 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 0.124 ] [ 0.00 , 0.133 ], [ 0.490E-01, 0.511E-01 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 0.250E-01 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.490E-01, 0.511E-01 ] [ 0.00 , 0.248E-01 ], [ 0.00 , 1.00 ] Fritz John multipliers V: [ -0.153 , -0.147 ], [ -0.255E-01, -0.245E-01 ] [ 0.245E-01, 0.255E-01 ], [ 0.218 , 0.249 ] [ 0.319 , 0.332 ], [ -0.562 , -0.539 ] [ -0.255 , -0.245 ] INEQ_CERT_FEASIBLE: F F F T T T T F T T F T T F F T NIN_POSS_BINDING: 7 ------------------------------------------------- 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: 34796 Number of bisections: 191484 No. dense interval residual evaluations -- gradient code list: 4692153 Number of orig. system inverse midpoint preconditioner rows: 27448426 Number of orig. system C-LP preconditioner rows: 4506906 Number of solutions for a component in the expanded system: 99483221 Total number of forward_substitutions: 20865412 Number of Gauss--Seidel steps on the dense system: 38802614 Number point dense residual evaluations, gradient codelist: 5971 Number of gradient evaluations from a gradient code list: 1324303 Total number of dense slope matrix evaluations: 19714410 Total number second-order interval evaluations of the original function: 408666 Total number dense interval constraint evaluations: 208153678 Total number dense interval constraint gradient component evaluations: 1703825280 Total number dense point constraint gradient component evaluations: 8808816 Total number dense interval reduced gradient evaluations: 6480330 Total number of calls to FRITZ_JOHN_RESIDUALS: 1631353 Number of times a box was rejected because the constraints were not satisfied: 457 Number of times a box was rejected because the gradient or reduced gradient did not contain zero: 22540 Average number of overall loop iterations in each call to the reduced interval Newton method): 5.55 Number of times a box was rejected in the interval Newton method due to an empty intersection: 64302 Number of times the interval Newton method made a coordinate interval smaller: 4738289 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 521842 Number of times a pivoting preconditioner was successful after the first sweep: 444109 Number of times a midpoint matrix was factored: 1208889 Total number of times the reduced interval Newton method was tried: 297215 Number of times an inverse midpoint preconditioner led to improvement or rejection: 2354848 Number of times a C LP preconditioner led to improvement or rejection: 1925901 Number of times computing a C_LP failed 3527 N_C_LP_INFEASIBLE = 164289 N_LPF_INF_OR_UNB = 164289 Number of possible splits as detected by the pivoting preconditioner: 1608812 Total time spent in the LP filter (creating and solving the LP): 893. Total time spent in subsit (constraint propagation): 41.0 Total time spent in reduced_interval_Newton (iteration to reduce the box): 0.600E+04 Total time spent actually solving the linear relaxations: 826. Total time spent doing linear algebra (preconditioners and solution processes): 0.483E+04 Total time spent running the approximate optimizer: 1.40 LIST_BOOKKEEPING_TIME: 103. FUNCTION_EVALUATION_TIME (in forward_substitution): 116. Time spent setting up pivoting preconditioners: 225. Time spent computing pivoting preconditioners: 129. Time spent computing LP preconditioners: 0.127E+04 Time spent computing inverse midpoint preconditioners: 135. Number of times MAXIT was exceeded in C_LP_DENSE: 55595 Number of unbounded problems found in C_LP_DENSE: 3527 Number of times the approximate solver was called: 142 Number Fritz-John matrix evaluations: 1608812 Number of times SUBSIT decreased one or more coordinate widths: 201050 Number of times SUBSIT rejected a box: 49689 Number times a box was rejected due infeasible inequality constraints: 18573 Total number of boxes processed in loop: 346904 BEST_ESTIMATE: 0.100E+05 Overall CPU time: 0.720E+04 CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 0.600E+04 =================================================== =================================================== 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: 34796 Interval hull of the small unverified boxes: [ 0.00 , 0.150E-02 ], [ 99.9 , 100. ] [ 0.999 , 1.00 ], [ 0.260E+04, 0.260E+04 ] [ 0.300E+04, 0.300E+04 ], [ 0.00 , 0.150E-02 ] [ 99.9 , 100. ], [ 99.9 , 100. ] [ 0.00 , 0.150E-02 ], [ 200. , 200. ] [ 0.00 , 0.150E-02 ], [ 99.9 , 100. ] Interval hull of the unfathomed boxes: [ 0.00 , 100. ], [ 0.00 , 200. ] [ 0.00 , 0.100E+05 ], [ 0.00 , 0.600E+04 ] [ 0.00 , 0.390E+04 ], [ 0.00 , 300. ] [ 0.00 , 300. ], [ 0.00 , 300. ] [ 0.00 , 100. ], [ 0.00 , 200. ] [ 0.00 , 100. ], [ 0.00 , 200. ] Rigorously verified bounds on the optimum, provided an optimum exists: [ -406. , 0.600E+04 ] FIRST UNFINISHED BOX: Box coordinates: [ 50.0 , 50.1 ], [ 0.00 , 0.678E-16 ] [ 3.00 , 3.00 ], [ 800. , 800. ] [ 900. , 900. ], [ 50.0 , 50.0 ] [ 0.206E-01, 0.220E-01 ], [ 49.9 , 50.0 ] [ 100. , 100. ], [ 0.00 , 0.878E-16 ] [ 49.9 , 50.0 ], [ 0.00 , 0.738E-16 ] PHI: [ -100. , -100. ] Box does not contain an approximate root. Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.00 , 0.190E-16 ] Fritz John multipliers U: [ 0.00 , 0.821E-16 ], [ 0.330 , 0.397 ] [ 0.00 , 1.00 ], [ 0.380 , 0.516 ] [ 0.00 , 1.00 ], [ 0.00 , 0.117 ] [ 0.00 , 0.667E-01 ], [ 0.00 , 1.00 ] [ 0.00 , 0.759E-01 ], [ 0.00 , 0.500 ] [ 0.00 , 0.165 ], [ 0.00 , 0.242E-16 ] [ 0.00 , 0.201 ], [ 0.00 , 1.00 ] [ 0.00 , 0.709 ], [ 0.00 , 0.173 ] Fritz John multipliers V: [ -0.707E-17, 0.769E-17 ], [ -0.190E-16, 0.205E-16 ] [ -0.205E-16, 0.189E-16 ], [ -0.123E-16, 0.113E-16 ] [ -0.400E-13, 0.201 ], [ -0.306E-16, 0.331E-16 ] [ -0.146E-16, 0.159E-16 ] INEQ_CERT_FEASIBLE: F F T F T T T T T T T F F T T F NIN_POSS_BINDING: 6 LAST UNFINISHED BOX: Box coordinates: [ 0.00 , 100. ], [ 0.00 , 200. ] [ 0.00 , 9.77 ], [ 0.300E+04, 0.600E+04 ] [ 0.00 , 0.195E+04 ], [ 0.00 , 300. ] [ 0.00 , 300. ], [ 0.00 , 300. ] [ 0.00 , 100. ], [ 0.00 , 200. ] [ 0.00 , 100. ], [ 0.00 , 200. ] PHI: [ 0.105E+04, 0.600E+04 ] Box does not contain an approximate root. Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.00 , 0.119 ] 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 , 0.205 ] [ 0.00 , 0.100 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 0.170 ], [ 0.00 , 1.00 ] [ 0.00 , 0.500 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] Fritz John multipliers V: [ -0.619 , 0.381 ], [ -0.119 , 0.930E-15 ] [ -0.312E-14, 0.133 ], [ -1.00 , 1.00 ] [ -1.00 , 1.00 ], [ -1.00 , 1.00 ] [ -1.00 , 1.00 ] INEQ_CERT_FEASIBLE: F F F F F T F F F F F F F F F F NIN_POSS_BINDING: 15 Total volume of the boxes that have not yet been processed: 1.29060381932493685E+028