Output from FIND_GLOBAL_MIN on 05/06/2012 at 22:14:27. Version for the system is: March 13, 2009 Codelist file name is: ex9_2_8G.CDL Box data file name is: ex9_2_8.DT1 Initial box: [ 0.00 , 20.0 ], [ 0.00 , 20.0 ] [ 0.00 , 0.00 ], [ 0.00 , 0.00 ] [ 0.00 , 1.00 ], [ 0.00 , 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: [ 0.997 , 0.999 ], [ 0.953E-03, 0.295E-02 ] [ 0.00 , 0.00 ], [ 0.00 , 0.00 ] [ 0.249 , 0.251 ], [ 0.997 , 0.999 ] PHI: [ 3.49 , 3.51 ] Box contains the following approximate root: 0.998 , 0.195E-02, 0.00 , 0.00 , 0.250 , 0.998 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 3.50 , 3.50 ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.00 , 0.297E-28 ] Fritz John multipliers U: [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 0.162E-16 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ] Fritz John multipliers V: [ -0.252E-16, 0.126E-16 ], [ -0.168E-25, 0.953E-26 ] [ -0.764E-30, 0.764E-30 ], [ -0.381E-28, 0.211E-28 ] [ -0.929E-29, 0.164E-28 ], [ -1.00 , 1.00 ] [ -1.00 , 1.00 ] INEQ_CERT_FEASIBLE: T T T T T T T NIN_POSS_BINDING: 0 ------------------------------------------------- THERE WERE NO BOXES CORRESPONDING TO VERIFIED FEASIBLE POINTS. ALGORITHM COMPLETED WITH LESS THAN THE MAXIMUM NUMBER, 500000 OF BOXES. Number of bisections: 9586 No. dense interval residual evaluations -- gradient code list: 155929 Number of orig. system C-LP preconditioner rows: 39808 Number of solutions for a component in the expanded system: 1445 Total number of forward_substitutions: 685116 Number of Gauss--Seidel steps on the dense system: 40649 Number of gradient evaluations from a gradient code list: 48865 Total number of dense slope matrix evaluations: 153047 Total number second-order interval evaluations of the original function: 33845 Total number dense interval constraint evaluations: 2276960 Total number dense interval constraint gradient component evaluations: 7465920 Total number dense point constraint gradient component evaluations: 11340 Total number dense interval reduced gradient evaluations: 79468 Total number of calls to FRITZ_JOHN_RESIDUALS: 19867 Average number of overall loop iterations in each call to the reduced interval Newton method): 2.04 Number of times the interval Newton method made a coordinate interval smaller: 20073 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 19825 Number of times a pivoting preconditioner was successful after the first sweep: 462 Number of times a midpoint matrix was factored: 9825 Total number of times the reduced interval Newton method was tried: 9727 Number of times a C LP preconditioner led to improvement or rejection: 248 Number of possible splits as detected by the pivoting preconditioner: 19867 Total time spent in the LP filter (creating and solving the LP): 18.2 Total time spent in subsit (constraint propagation): 0.124 Total time spent in reduced_interval_Newton (iteration to reduce the box): 7.55 Total time spent actually solving the linear relaxations: 16.7 Total time spent doing linear algebra (preconditioners and solution processes): 3.62 LIST_BOOKKEEPING_TIME: 0.796 FUNCTION_EVALUATION_TIME (in forward_substitution): 2.41 Time spent setting up pivoting preconditioners: 0.996 Time spent computing pivoting preconditioners: 0.708 Time spent computing LP preconditioners: 1.07 Time spent computing inverse midpoint preconditioners: 0.800E-01 Number of times the approximate solver was called: 1 Number Fritz-John matrix evaluations: 19867 Number of times SUBSIT decreased one or more coordinate widths: 63 Total number of boxes processed in loop: 10098 BEST_ESTIMATE: 0.300E+05 Overall CPU time: 30.9 CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 7.55 =================================================== =================================================== 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: 0 Interval hull of the small unverified boxes: [ 0.997 , 0.999 ], [ 0.953E-03, 0.295E-02 ] [ 0.00 , 0.00 ], [ 0.00 , 0.00 ] [ 0.249 , 0.251 ], [ 0.997 , 0.999 ] Rigorously verified bounds on the optimum, provided an optimum exists: [ 3.49 , 3.51 ]