Output from FIND_GLOBAL_MIN on 05/07/2012 at 02:18:46. Version for the system is: March 13, 2009 Codelist file name is: ex14_1_2G.CDL Box data file name is: ex14_1_2.DT1 Initial box: [ 0.100E-03, 100. ], [ 0.100E-03, 100. ] [ 0.100E-03, 100. ], [ 0.100E-03, 100. ] [ 0.100E-03, 100. ], [ -0.100E+05, 0.100E+05 ] BOUND_CONSTRAINT: 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: [ 0.243E-02, 0.443E-02 ], [ 31.3 , 31.4 ] [ 0.674E-01, 0.694E-01 ], [ 0.859 , 0.861 ] [ 0.360E-01, 0.380E-01 ], [ -0.100E-02, 0.100E-02 ] PHI: [ -0.100E-02, 0.100E-02 ] Box contains the following approximate root: 0.343E-02, 31.3 , 0.684E-01, 0.860 , 0.370E-01, -0.993E-08 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ -0.993E-08, -0.993E-08 ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.500 , 0.500 ] Fritz John multipliers U: [ 0.00 , 0.505 ], [ 0.00 , 0.505 ] [ 0.00 , 0.505 ], [ 0.00 , 0.505 ] [ 0.00 , 0.505 ], [ 0.00 , 0.505 ] [ 0.00 , 0.505 ], [ 0.00 , 0.505 ] [ 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: [ -0.643E-05, 0.643E-05 ] INEQ_CERT_FEASIBLE: F F F F F F F F T T T T T T T T T T NIN_POSS_BINDING: 8 ------------------------------------------------- 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: 15392 Number of bisections: 341615 No. dense interval residual evaluations -- gradient code list: 6204172 Number of orig. system inverse midpoint preconditioner rows: 15743562 Number of orig. system C-LP preconditioner rows: 3235195 Number of solutions for a component in the expanded system: 1449623 Total number of forward_substitutions: 22760206 Number of Gauss--Seidel steps on the dense system: 19407725 Number point dense residual evaluations, gradient codelist: 1049831 Number of gradient evaluations from a gradient code list: 1995920 Total number of dense slope matrix evaluations: 11168934 Total number second-order interval evaluations of the original function: 737004 Total number dense interval constraint evaluations: 222248922 Total number dense interval constraint gradient component evaluations: 823361580 Total number dense point constraint gradient component evaluations: 117403242 Total number dense interval reduced gradient evaluations: 6901684 Total number of calls to FRITZ_JOHN_RESIDUALS: 1749240 Number of times a box was rejected because the constraints were not satisfied: 34 Number of times a box was rejected because the gradient or reduced gradient did not contain zero: 10585 Number of times a box was rejected due to infeasibility in LP_FILTER: 1931 Average number of overall loop iterations in each call to the reduced interval Newton method): 3.91 Number of times a box was rejected in the interval Newton method due to an empty intersection: 90385 Number of times the interval Newton method made a coordinate interval smaller: 3283703 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 1425025 Number of times a pivoting preconditioner was successful after the first sweep: 1054268 Number of times a midpoint matrix was factored: 1104061 Total number of times the reduced interval Newton method was tried: 436170 Number of times an inverse midpoint preconditioner led to improvement or rejection: 1357513 Number of times a C LP preconditioner led to improvement or rejection: 146914 Number of times computing a C_LP failed 7570 N_C_LP_INFEASIBLE = 318934 N_REJECT_WITH_LP filter = 1963 N_LPF_INF_OR_UNB = 318590 Number of possible splits as detected by the pivoting preconditioner: 1664549 Total time spent in the LP filter (creating and solving the LP): 0.354E+04 Total time spent in subsit (constraint propagation): 10.9 Total time spent in reduced_interval_Newton (iteration to reduce the box): 0.179E+04 Total time spent searching for "D" in the LP filter: 28.8 Total time spent actually solving the linear relaxations: 0.327E+04 Total time spent doing linear algebra (preconditioners and solution processes): 0.118E+04 Total time spent running the approximate optimizer: 0.700 LIST_BOOKKEEPING_TIME: 158. FUNCTION_EVALUATION_TIME (in forward_substitution): 336. Time spent setting up pivoting preconditioners: 109. Time spent computing pivoting preconditioners: 111. Time spent computing LP preconditioners: 152. Time spent computing inverse midpoint preconditioners: 54.8 Number of times MAXIT was exceeded in C_LP_DENSE: 14365 Number of unbounded problems found in C_LP_DENSE: 7571 Number of times the approximate solver was called: 37053 Number Fritz-John matrix evaluations: 1738655 Number of times SUBSIT decreased one or more coordinate widths: 1606 Number of times SUBSIT rejected a box: 190 Number times a box was rejected due infeasible inequality constraints: 30625 Total number of boxes processed in loop: 438345 BEST_ESTIMATE: 0.100E+05 Overall CPU time: 0.720E+04 CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 0.179E+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: 15392 Interval hull of the small unverified boxes: [ 0.243E-02, 0.443E-02 ], [ 31.3 , 31.4 ] [ 0.674E-01, 0.694E-01 ], [ 0.859 , 0.861 ] [ 0.360E-01, 0.380E-01 ], [ -0.100E-02, 0.100E-02 ] Interval hull of the unfathomed boxes: [ 0.100E-03, 100. ], [ 0.100E-03, 100. ] [ 0.100E-03, 100. ], [ 0.100E-03, 83.7 ] [ 0.100E-03, 100. ], [ 0.103E-03, 0.100E+05 ] Rigorously verified bounds on the optimum, provided an optimum exists: [ -0.100E-02, 0.100E+05 ] FIRST UNFINISHED BOX: Box coordinates: [ 0.350E-02, 0.350E-02 ], [ 30.7 , 30.7 ] [ 0.690E-01, 0.690E-01 ], [ 0.859 , 0.860 ] [ 0.369E-01, 0.370E-01 ], [ 0.103E-03, 0.265E-03 ] PHI: [ 0.103E-03, 0.265E-03 ] Box does not contain an approximate root. Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.434 , 0.566 ] Fritz John multipliers U: [ 0.00 , 0.698 ], [ 0.00 , 0.698 ] [ 0.00 , 0.698 ], [ 0.00 , 0.698 ] [ 0.00 , 0.698 ], [ 0.00 , 0.698 ] [ 0.00 , 0.698 ], [ 0.00 , 0.113E-02 ] [ 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: [ -0.257 , 0.257 ] INEQ_CERT_FEASIBLE: T F T F F F T F T T T T T T T T T T NIN_POSS_BINDING: 5 LAST UNFINISHED BOX: Box coordinates: [ 0.100E-03, 6.00 ], [ 50.0 , 100. ] [ 0.100E-03, 6.25 ], [ 0.100E-03, 83.7 ] [ 0.100E-03, 100. ], [ 0.500E+04, 0.100E+05 ] PHI: [ 0.500E+04, 0.100E+05 ] 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 , 0.880 ], [ 0.00 , 0.880 ] [ 0.00 , 0.917 ], [ 0.00 , 0.917 ] [ 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 ] INEQ_CERT_FEASIBLE: F F F F F F F F F T T F F T F T F F NIN_POSS_BINDING: 14 Total volume of the boxes that have not yet been processed: 13392623912175.797