Output from FIND_GLOBAL_MIN on 05/07/2012 at 06:39:04. Version for the system is: March 13, 2009 Codelist file name is: ex7_3_5_sourceG.CDL Box data file name is: ex7_3_5_source.DT1 Initial box: [ -0.100E+05, 0.100E+05 ], [ -0.100E+05, 0.100E+05 ] [ 0.00 , 10.0 ], [ -0.100E+05, 0.100E+05 ] [ -0.100E+05, 0.100E+05 ], [ -0.100E+05, 0.100E+05 ] [ -0.100E+05, 0.100E+05 ], [ -0.100E+05, 0.100E+05 ] [ -0.100E+05, 0.100E+05 ], [ -0.100E+05, 0.100E+05 ] [ -0.100E+05, 0.100E+05 ], [ -0.100E+05, 0.100E+05 ] [ -0.100E+05, 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 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: [ 0.572 , 0.574 ], [ 0.610 , 0.612 ] [ 2.40 , 2.40 ], [ 1.76 , 1.76 ] [ 1.44 , 1.45 ], [ 0.349 , 0.351 ] [ 0.195 , 0.197 ], [ 0.145E-01, 0.165E-01 ] [ -0.384E-03, 0.162E-02 ], [ -0.988E-03, 0.101E-02 ] [ 2.74 , 2.74 ], [ 1.48 , 1.49 ] [ 1.94 , 1.94 ] PHI: [ 2.74 , 2.74 ] Box contains the following approximate root: 0.573 , 0.611 , 2.40 , 1.76 , 1.44 , 0.350 0.196 , 0.155E-01, 0.616E-03, 0.122E-04, 2.74 , 1.48 1.94 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 2.74 , 2.74 ] 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 ] 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 ] [ -1.00 , 1.00 ] INEQ_CERT_FEASIBLE: F F F F F F NIN_POSS_BINDING: 6 ------------------------------------------------- ALGORITHM COULD NOT COMPLETE IN 0.7200D+04 SECONDS OF CPU TIME. Number of boxes that have not yet been processed: 77643 Number of bisections: 132254 No. dense interval residual evaluations -- gradient code list: 1940343 Number of orig. system inverse midpoint preconditioner rows: 6112293 Number of orig. system C-LP preconditioner rows: 3761597 Number of solutions for a component in the expanded system: 91987671 Total number of forward_substitutions: 10497075 Number of Gauss--Seidel steps on the dense system: 11988370 Number point dense residual evaluations, gradient codelist: 1562 Number of gradient evaluations from a gradient code list: 706940 Total number of dense slope matrix evaluations: 3880392 Total number second-order interval evaluations of the original function: 264728 Total number dense interval constraint evaluations: 42721201 Total number dense interval constraint gradient component evaluations: 340632890 Total number dense point constraint gradient component evaluations: 182455 Total number dense interval reduced gradient evaluations: 1112497 Total number of calls to FRITZ_JOHN_RESIDUALS: 278128 Number of times a box was rejected because the constraints were not satisfied: 7355 Number of times feasible point was found based on the LP_FILTER approximate solution: 1 Average number of overall loop iterations in each call to the reduced interval Newton method): 2.04 Number of times a box was rejected in the interval Newton method due to an empty intersection: 394 Number of times the interval Newton method made a coordinate interval smaller: 411926 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 139740 Number of times a pivoting preconditioner was successful after the first sweep: 74107 Number of times a midpoint matrix was factored: 217102 Total number of times the reduced interval Newton method was tried: 140003 Number of times an inverse midpoint preconditioner led to improvement or rejection: 4807 Number of times a C LP preconditioner led to improvement or rejection: 267619 Number of times computing a C_LP failed 5826 N_C_LP_INFEASIBLE = 101453 N_NEW_BEST_ESTIMATE_WITH_LP filter = 1 N_LPF_INF_OR_UNB = 101452 Number of possible splits as detected by the pivoting preconditioner: 278113 Total time spent in the LP filter (creating and solving the LP): 0.302E+04 Total time spent in subsit (constraint propagation): 52.7 Total time spent in reduced_interval_Newton (iteration to reduce the box): 0.286E+04 Total time spent searching for "D" in the LP filter: 207. Total time spent actually solving the linear relaxations: 0.262E+04 Total time spent doing linear algebra (preconditioners and solution processes): 0.194E+04 Total time spent running the approximate optimizer: 0.200E-01 LIST_BOOKKEEPING_TIME: 914. FUNCTION_EVALUATION_TIME (in forward_substitution): 169. Time spent setting up pivoting preconditioners: 59.9 Time spent computing pivoting preconditioners: 25.5 Time spent computing LP preconditioners: 600. Time spent computing inverse midpoint preconditioners: 35.4 Number of times MAXIT was exceeded in C_LP_DENSE: 393 Number of unbounded problems found in C_LP_DENSE: 5834 Number of times the approximate solver was called: 7 Number Fritz-John matrix evaluations: 278128 Number of times SUBSIT decreased one or more coordinate widths: 54752 Number of times SUBSIT rejected a box: 22421 Total number of boxes processed in loop: 162425 N_FINDOPT_SUCCESS = 1 BEST_ESTIMATE: 2.74 Overall CPU time: 0.720E+04 CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 0.286E+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: 77643 Interval hull of the boxes verified to contain feasible points or critical points: [ 0.572 , 0.574 ], [ 0.610 , 0.612 ] [ 2.40 , 2.40 ], [ 1.76 , 1.76 ] [ 1.44 , 1.45 ], [ 0.349 , 0.351 ] [ 0.195 , 0.197 ], [ 0.145E-01, 0.165E-01 ] [ -0.384E-03, 0.162E-02 ], [ -0.988E-03, 0.101E-02 ] [ 2.74 , 2.74 ], [ 1.48 , 1.49 ] [ 1.94 , 1.94 ] Interval hull of the unfathomed boxes: [ -43.6 , 43.6 ], [ -0.150E+04, 0.150E+04 ] [ 0.00 , 10.0 ], [ -0.100E+05, 0.100E+05 ] [ -0.100E+05, 0.100E+05 ], [ -0.100E+05, 0.100E+05 ] [ -0.327E+04, 0.100E+05 ], [ -83.0 , 0.100E+05 ] [ -0.706 , 0.100E+05 ], [ -0.223-299, 0.100E+05 ] [ -0.457E-12, 0.100E+05 ], [ -0.223-307, 0.859E+04 ] [ -15.9 , 0.100E+05 ] Rigorously verified bounds on the optimum, provided an optimum exists: [ 2.74 , 2.74 ] FIRST UNFINISHED BOX: Box coordinates: [ 0.179 , 0.573 ], [ 0.200 , 0.611 ] [ 9.53 , 9.69 ], [ 0.113 , 0.936 ] [ 0.652E-01, 1.06 ], [ 0.986E-01, 0.110 ] [ 0.119E-01, 0.221E-01 ], [ 0.127E-02, 0.138E-02 ] [ 0.134E-03, 0.194E-03 ], [ 0.230E-05, 0.306E-05 ] [ -0.457E-12, 39.1 ], [ 0.146 , 1.48 ] [ 0.235 , 1.94 ] PHI: [ -0.457E-12, 39.1 ] Box does not contain an approximate root. Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.00 , 0.301 ] Fritz John multipliers U: [ 0.00 , 1.00 ], [ 0.00 , 0.850E-02 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] Fritz John multipliers V: [ -0.147E-07, 0.147E-07 ], [ -0.134E-05, 0.134E-05 ] [ -0.139E-05, 0.139E-05 ], [ -0.148E-07, 0.148E-07 ] [ -0.126E-03, 0.126E-03 ], [ -0.131E-03, 0.131E-03 ] [ -1.00 , 1.00 ], [ -0.118E-01, 0.118E-01 ] [ -1.00 , 1.00 ], [ -0.133E-05, 0.133E-05 ] [ -0.123E-01, 0.123E-01 ] INEQ_CERT_FEASIBLE: T F F F T T NIN_POSS_BINDING: 3 LAST UNFINISHED BOX: Box coordinates: [ 0.572 , 0.574 ], [ 0.610 , 0.612 ] [ 2.40 , 2.40 ], [ 1.76 , 1.76 ] [ 1.44 , 1.45 ], [ 0.349 , 0.351 ] [ 0.195 , 0.197 ], [ 0.145E-01, 0.165E-01 ] [ 0.239E-04, 0.162E-02 ], [ 0.463E-06, 0.101E-02 ] [ 2.74 , 2.74 ], [ 1.48 , 1.49 ] [ 1.94 , 2.69 ] PHI: [ 2.74 , 2.74 ] Box does not contain an approximate root. Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.00 , 0.295 ] 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 ] Fritz John multipliers V: [ -0.191E-02, 0.191E-02 ], [ -0.913E-02, 0.913E-02 ] [ -0.119E-01, 0.119E-01 ], [ -0.191E-02, 0.191E-02 ] [ -0.570E-01, 0.570E-01 ], [ -0.745E-01, 0.745E-01 ] [ -1.00 , 1.00 ], [ -0.357 , 0.357 ] [ -1.00 , 1.00 ], [ -0.913E-02, 0.913E-02 ] [ -0.466 , 0.466 ] INEQ_CERT_FEASIBLE: T F T F T T NIN_POSS_BINDING: 2 Total volume of the boxes that have not yet been processed: 6.76481732232324571E+046