Output from FIND_GLOBAL_MIN on 05/07/2012 at 09:02:49. Version for the system is: March 13, 2009 Codelist file name is: ex9_1_2G.CDL Box data file name is: ex9_1_2.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 , 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 --------------------------------------- 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: 195673 Number of bisections: 195702 No. dense interval residual evaluations -- gradient code list: 2776400 Number of orig. system inverse midpoint preconditioner rows: 13945 Number of orig. system C-LP preconditioner rows: 3327289 Number of solutions for a component in the expanded system: 1824969 Total number of forward_substitutions: 15582973 Number of Gauss--Seidel steps on the dense system: 3276605 Number point dense residual evaluations, gradient codelist: 20 Number of gradient evaluations from a gradient code list: 978539 Total number of dense slope matrix evaluations: 3336169 Total number second-order interval evaluations of the original function: 539669 Total number dense interval constraint evaluations: 61596400 Total number dense interval constraint gradient component evaluations: 345322910 Total number dense point constraint gradient component evaluations: 41990 Total number dense interval reduced gradient evaluations: 1118600 Total number of calls to FRITZ_JOHN_RESIDUALS: 279650 Average number of overall loop iterations in each call to the reduced interval Newton method): 1.43 Number of times the interval Newton method made a coordinate interval smaller: 84471 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 84240 Number of times a pivoting preconditioner was successful after the first sweep: 281 Number of times a midpoint matrix was factored: 195797 Total number of times the reduced interval Newton method was tried: 195702 Number of times an inverse midpoint preconditioner led to improvement or rejection: 10 Number of times a C LP preconditioner led to improvement or rejection: 221 Number of times computing a C_LP failed 66181 Number of possible splits as detected by the pivoting preconditioner: 279650 Total time spent in the LP filter (creating and solving the LP): 383. Total time spent in subsit (constraint propagation): 3.79 Total time spent in reduced_interval_Newton (iteration to reduce the box): 0.208E+04 Total time spent actually solving the linear relaxations: 348. Total time spent doing linear algebra (preconditioners and solution processes): 0.123E+04 Total time spent running the approximate optimizer: 0.800E-02 LIST_BOOKKEEPING_TIME: 0.459E+04 FUNCTION_EVALUATION_TIME (in forward_substitution): 80.2 Time spent setting up pivoting preconditioners: 72.9 Time spent computing pivoting preconditioners: 28.2 Time spent computing LP preconditioners: 926. Time spent computing inverse midpoint preconditioners: 23.8 Number of times MAXIT was exceeded in C_LP_DENSE: 35 Number of unbounded problems found in C_LP_DENSE: 66181 Number of times the approximate solver was called: 1 Number Fritz-John matrix evaluations: 279650 Number of times SUBSIT decreased one or more coordinate widths: 113497 Number of times SUBSIT rejected a box: 29 Number times a box was rejected due infeasible inequality constraints: 1 Total number of boxes processed in loop: 195731 BEST_ESTIMATE: 0.445-307 Overall CPU time: 0.720E+04 CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 0.208E+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: 195673 Interval hull of the unfathomed boxes: [ 1.41 , 6.00 ], [ 0.00 , 12.0 ] [ 0.00 , 12.0 ], [ 0.00 , 4.00 ] [ 0.00 , 0.223-307 ], [ 0.00 , 0.500E+04 ] [ 0.00 , 0.100E+05 ], [ 0.00 , 1.00 ] [ 0.00 , 4.00 ], [ 0.00 , 4.00 ] Rigorously verified bounds on the optimum, provided an optimum exists: [ -16.0 , 0.445-307 ] FIRST UNFINISHED BOX: Box coordinates: [ 3.00 , 3.00 ], [ 0.00 , 0.223-307 ] [ 0.00 , 0.223-307 ], [ 4.00 , 4.00 ] [ 0.00 , 0.223-307 ], [ 0.486E+04, 0.486E+04 ] [ 0.971E+04, 0.971E+04 ], [ 0.00 , 0.223-307 ] [ 4.00 , 4.00 ], [ 4.00 , 4.00 ] PHI: [ -16.0 , -16.0 ] Box does not contain an approximate root. Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.00 , 0.692 ] 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 ] Fritz John multipliers V: [ -0.597E-14, 0.333 ], [ -0.213E-03, 0.213E-03 ] [ -0.179E-05, 0.111E-03 ], [ -0.269E-14, 0.250 ] [ -0.117-302, 0.117-302 ], [ -0.105E-12, 1.00 ] [ -0.769E-01, 0.127E-12 ], [ -0.136-302, 0.136-302 ] [ -0.585-303, 0.585-303 ] INEQ_CERT_FEASIBLE: T F F T F T T F T T NIN_POSS_BINDING: 4 LAST UNFINISHED BOX: Box coordinates: [ 3.00 , 4.12 ], [ 10.9 , 12.0 ] [ 7.50 , 12.0 ], [ 0.00 , 0.223-307 ] [ 0.00 , 0.223-307 ], [ 0.00 , 0.223-307 ] [ 0.00 , 0.223-307 ], [ 1.00 , 1.00 ] [ 0.00 , 0.562 ], [ 0.00 , 0.223-307 ] PHI: [ -0.562 , 0.445-307 ] Box does not contain an approximate root. Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.00 , 0.308 ] 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 , 0.134E-14 ], [ 0.00 , 1.00 ] Fritz John multipliers V: [ -0.625E-01, 0.333 ], [ -0.476E-02, 0.920E-01 ] [ -0.280E-01, 0.133 ], [ -0.213E-13, 1.00 ] [ -0.246-305, 0.244-305 ], [ -0.382E-16, 0.725E-16 ] [ -0.345E-16, 0.124E-16 ], [ -1.00 , 0.129E-13 ] [ -0.493E-31, 0.493E-31 ] INEQ_CERT_FEASIBLE: T T T F F F F T F F NIN_POSS_BINDING: 6 Total volume of the boxes that have not yet been processed: 0.0000000000000000