Output from FIND_GLOBAL_MIN on 05/07/2012 at 00:18:19. Version for the system is: March 13, 2009 Codelist file name is: ex8_1_7_sourceG.CDL Box data file name is: ex8_1_7_source.DT1 Initial box: [ -5.00 , 5.00 ], [ -5.00 , 5.00 ] [ -5.00 , 5.00 ], [ -5.00 , 5.00 ] [ -5.00 , 5.00 ] BOUND_CONSTRAINT: 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. 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: 171133 Number of bisections: 481941 No. dense interval residual evaluations -- gradient code list: 6625582 Number of orig. system inverse midpoint preconditioner rows: 8823387 Number of orig. system C-LP preconditioner rows: 5551785 Number of solutions for a component in the expanded system: 162723 Total number of forward_substitutions: 23239053 Number of Gauss--Seidel steps on the dense system: 17896448 Number point dense residual evaluations, gradient codelist: 1082161 Number of gradient evaluations from a gradient code list: 2409909 Total number of dense slope matrix evaluations: 6768510 Total number second-order interval evaluations of the original function: 1005550 Total number dense interval constraint evaluations: 156734846 Total number dense interval constraint gradient component evaluations: 443201550 Total number dense point constraint gradient component evaluations: 74865525 Total number dense interval reduced gradient evaluations: 4568687 Total number of calls to FRITZ_JOHN_RESIDUALS: 1152592 Number of times a box was rejected due to infeasibility in LP_FILTER: 79 Average number of overall loop iterations in each call to the reduced interval Newton method): 2.31 Number of times a box was rejected in the interval Newton method due to an empty intersection: 41663 Number of times the interval Newton method made a coordinate interval smaller: 973805 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 308822 Number of times a pivoting preconditioner was successful after the first sweep: 182010 Number of times a midpoint matrix was factored: 802113 Total number of times the reduced interval Newton method was tried: 481941 Number of times a C LP preconditioner led to improvement or rejection: 456529 Number of times computing a C_LP failed 579 N_C_LP_INFEASIBLE = 88990 N_REJECT_WITH_LP filter = 88 N_LPF_INF_OR_UNB = 88892 Number of possible splits as detected by the pivoting preconditioner: 1110911 Total time spent in the LP filter (creating and solving the LP): 0.144E+04 Total time spent in subsit (constraint propagation): 8.00 Total time spent in reduced_interval_Newton (iteration to reduce the box): 0.122E+04 Total time spent searching for "D" in the LP filter: 30.0 Total time spent actually solving the linear relaxations: 0.125E+04 Total time spent doing linear algebra (preconditioners and solution processes): 871. Total time spent running the approximate optimizer: 0.660 LIST_BOOKKEEPING_TIME: 0.314E+04 FUNCTION_EVALUATION_TIME (in forward_substitution): 212. Time spent setting up pivoting preconditioners: 43.1 Time spent computing pivoting preconditioners: 49.9 Time spent computing LP preconditioners: 418. Time spent computing inverse midpoint preconditioners: 27.2 Number of times MAXIT was exceeded in C_LP_DENSE: 321192 Number of unbounded problems found in C_LP_DENSE: 579 Number of times the approximate solver was called: 41669 Number Fritz-John matrix evaluations: 1152592 Number of times SUBSIT decreased one or more coordinate widths: 769 Number of times SUBSIT rejected a box: 16 Number times a box was rejected due infeasible inequality constraints: 4 Total number of boxes processed in loop: 482049 BEST_ESTIMATE: 0.211E+05 Overall CPU time: 0.720E+04 CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 0.122E+04 =================================================== =================================================== Number of boxes in the list with proven feasible points: 0 Number of boxes in the list of other small boxes: 0 Number of unfathomed boxes: 171133 Interval hull of the unfathomed boxes: [ -5.00 , 5.00 ], [ -4.17 , 5.00 ] [ -2.87 , 2.24 ], [ -5.00 , 5.00 ] [ -2.70 , 5.00 ] Rigorously verified bounds on the optimum, provided an optimum exists: [ 0.231E-01, 0.140E+05 ] FIRST UNFINISHED BOX: Box coordinates: [ 1.11 , 1.11 ], [ 1.22 , 1.22 ] [ 1.54 , 1.54 ], [ 1.79 , 1.79 ] [ 1.98 , 1.98 ] PHI: [ 0.293E-01, 0.293E-01 ] Box does not contain an approximate root. Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.00 , 0.108E-02 ] Fritz John multipliers U: [ 0.00 , 0.500 ], [ 0.00 , 0.500 ] [ 0.00 , 0.500 ], [ 0.00 , 0.500 ] [ 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: [ -0.581E-07, 0.239E-04 ] INEQ_CERT_FEASIBLE: F F F F T T T T T T T T T T NIN_POSS_BINDING: 4 LAST UNFINISHED BOX: Box coordinates: [ -5.00 , -0.400 ], [ -4.17 , 5.00 ] [ -2.64 , 2.24 ], [ -5.00 , -2.70 ] [ 2.71 , 5.00 ] PHI: [ 593. , 0.140E+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 , 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 T T F T T F T T F NIN_POSS_BINDING: 8 Total volume of the boxes that have not yet been processed: 5294.8640233657134