Output from FIND_GLOBAL_MIN on 05/07/2012 at 08:58:50. Version for the system is: March 13, 2009 Codelist file name is: ex14_1_5G.CDL Box data file name is: ex14_1_5.DT1 Initial box: [ -2.00 , 2.00 ], [ -2.00 , 2.00 ] [ -2.00 , 2.00 ], [ -2.00 , 2.00 ] [ -2.00 , 2.00 ], [ -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: [ 0.999 , 1.00 ], [ 0.999 , 1.00 ] [ 0.999 , 1.00 ], [ 0.999 , 1.00 ] [ 0.999 , 1.00 ], [ -0.100E-02, 0.100E-02 ] PHI: [ -0.100E-02, 0.100E-02 ] Box contains the following approximate root: 1.00 , 1.00 , 1.00 , 1.00 , 1.00 , -0.998E-08 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ -0.998E-08, -0.998E-08 ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.500 , 0.500 ] Fritz John multipliers U: [ 0.250 , 0.250 ], [ 0.250 , 0.250 ] [ 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: [ -0.213E-14, 0.213E-14 ], [ -0.213E-14, 0.213E-14 ] [ -0.213E-14, 0.213E-14 ], [ -0.213E-14, 0.213E-14 ] INEQ_CERT_FEASIBLE: F F T T T T T T T T T T NIN_POSS_BINDING: 2 ------------------------------------------------- Box no.: 2 Box coordinates: [ 0.915 , 0.917 ], [ 0.915 , 0.917 ] [ 0.915 , 0.917 ], [ 0.915 , 0.917 ] [ 1.42 , 1.42 ], [ -0.100E-02, 0.100E-02 ] PHI: [ -0.100E-02, 0.100E-02 ] Box contains the following approximate root: 0.916 , 0.916 , 0.916 , 0.916 , 1.42 , -0.998E-08 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ -0.998E-08, -0.998E-08 ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.500 , 0.500 ] Fritz John multipliers U: [ 0.250 , 0.250 ], [ 0.250 , 0.250 ] [ 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: [ -0.293E-13, 0.294E-13 ], [ -0.293E-13, 0.294E-13 ] [ -0.293E-13, 0.293E-13 ], [ -0.293E-13, 0.293E-13 ] INEQ_CERT_FEASIBLE: F F T T T T T T T T T T NIN_POSS_BINDING: 2 ------------------------------------------------- Box no.: 3 Box coordinates: [ 0.959 , 0.961 ], [ 0.959 , 0.961 ] [ 0.959 , 0.961 ], [ 0.959 , 0.961 ] [ 1.20 , 1.20 ], [ 0.182E-01, 0.202E-01 ] PHI: [ 0.182E-01, 0.202E-01 ] Box contains the following approximate root: 1.00 , 1.00 , 1.00 , 1.00 , 1.00 , -0.998E-08 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ -0.998E-08, -0.998E-08 ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.479 , 0.479 ] Fritz John multipliers U: [ 0.479 , 0.479 ], [ 0.00 , 0.702 ] [ 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: [ -0.102 , -0.102 ], [ -0.102 , -0.102 ] [ -0.102 , -0.102 ], [ -0.102 , -0.102 ] INEQ_CERT_FEASIBLE: F T T T T T T T T T T T NIN_POSS_BINDING: 1 ------------------------------------------------- THERE WERE NO BOXES CORRESPONDING TO VERIFIED FEASIBLE POINTS. ALGORITHM COMPLETED WITH LESS THAN THE MAXIMUM NUMBER, 500000 OF BOXES. Number of bisections: 86 No. dense interval residual evaluations -- gradient code list: 2773 Number of orig. system inverse midpoint preconditioner rows: 7582 Number of orig. system C-LP preconditioner rows: 2451 Number of solutions for a component in the expanded system: 13729 Total number of forward_substitutions: 11082 Number of Gauss--Seidel steps on the dense system: 10522 Number point dense residual evaluations, gradient codelist: 557 Number of gradient evaluations from a gradient code list: 696 Total number of dense slope matrix evaluations: 6142 Total number second-order interval evaluations of the original function: 352 Total number dense interval constraint evaluations: 87428 Total number dense interval constraint gradient component evaluations: 352656 Total number dense point constraint gradient component evaluations: 59904 Total number dense interval reduced gradient evaluations: 3832 Total number of calls to FRITZ_JOHN_RESIDUALS: 1006 Number of times a box was rejected because the constraints were not satisfied: 1 Number of times a box was rejected because the gradient or reduced gradient did not contain zero: 38 Average number of overall loop iterations in each call to the reduced interval Newton method): 5.19 Number of times a box was rejected in the interval Newton method due to an empty intersection: 99 Number of times the interval Newton method made a coordinate interval smaller: 4500 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 685 Number of times a pivoting preconditioner was successful after the first sweep: 675 Number of times a midpoint matrix was factored: 616 Total number of times the reduced interval Newton method was tried: 173 Number of times an inverse midpoint preconditioner led to improvement or rejection: 2541 Number of times a C LP preconditioner led to improvement or rejection: 603 N_C_LP_INFEASIBLE = 6 N_LPF_INF_OR_UNB = 6 Number of possible splits as detected by the pivoting preconditioner: 855 Total time spent in the LP filter (creating and solving the LP): 0.456 Total time spent in subsit (constraint propagation): 0.400E-02 Total time spent in reduced_interval_Newton (iteration to reduce the box): 0.548 Total time spent actually solving the linear relaxations: 0.412 Total time spent doing linear algebra (preconditioners and solution processes): 0.380 LIST_BOOKKEEPING_TIME: 0.200E-01 FUNCTION_EVALUATION_TIME (in forward_substitution): 0.440E-01 Time spent setting up pivoting preconditioners: 0.280E-01 Time spent computing pivoting preconditioners: 0.480E-01 Time spent computing LP preconditioners: 0.320E-01 Time spent computing inverse midpoint preconditioners: 0.160E-01 Number of times the approximate solver was called: 55 Number Fritz-John matrix evaluations: 965 Number of times SUBSIT decreased one or more coordinate widths: 54 Number of times SUBSIT rejected a box: 5 Number times a box was rejected due infeasible inequality constraints: 1 Total number of boxes processed in loop: 178 BEST_ESTIMATE: 0.100E+05 Overall CPU time: 1.84 CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 0.548 =================================================== =================================================== Number of boxes in the list with proven feasible points: 0 Number of boxes in the list of other small boxes: 3 Number of unfathomed boxes: 0 Interval hull of the small unverified boxes: [ 0.915 , 1.00 ], [ 0.915 , 1.00 ] [ 0.915 , 1.00 ], [ 0.915 , 1.00 ] [ 0.999 , 1.42 ], [ -0.100E-02, 0.202E-01 ] Rigorously verified bounds on the optimum, provided an optimum exists: [ -0.100E-02, 0.202E-01 ]