Output from FIND_GLOBAL_MIN on 05/07/2012 at 08:58:43. Version for the system is: March 13, 2009 Codelist file name is: sampleG.CDL Box data file name is: sample.DT1 Initial box: [ 100. , 0.100E+05 ], [ 100. , 0.100E+05 ] [ 100. , 0.100E+05 ], [ 100. , 0.100E+05 ] BOUND_CONSTRAINT: 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: [ 193. , 194. ], [ 179. , 180. ] [ 185. , 185. ], [ 169. , 169. ] PHI: [ 726. , 727. ] Box contains the following approximate root: 193. , 180. , 185. , 169. OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 727. , 727. ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.203E-04, 0.203E-04 ] Fritz John multipliers U: [ 0.156 , 0.156 ], [ 0.843 , 0.843 ] [ 0.00 , 0.215 ], [ 0.00 , 1.00 ] [ 0.00 , 0.371E-03 ], [ 0.00 , 1.00 ] [ 0.00 , 0.123E-03 ], [ 0.00 , 1.00 ] [ 0.00 , 0.836E-04 ], [ 0.00 , 1.00 ] INEQ_CERT_FEASIBLE: F F T T T T T T T T NIN_POSS_BINDING: 2 ------------------------------------------------- THERE WERE NO BOXES CORRESPONDING TO VERIFIED FEASIBLE POINTS. ALGORITHM COMPLETED WITH LESS THAN THE MAXIMUM NUMBER, 500000 OF BOXES. Number of bisections: 432 No. dense interval residual evaluations -- gradient code list: 10423 Number of orig. system inverse midpoint preconditioner rows: 15720 Number of orig. system C-LP preconditioner rows: 3954 Number of solutions for a component in the expanded system: 9349 Total number of forward_substitutions: 32433 Number of Gauss--Seidel steps on the dense system: 21721 Number point dense residual evaluations, gradient codelist: 895 Number of gradient evaluations from a gradient code list: 3120 Total number of dense slope matrix evaluations: 13985 Total number second-order interval evaluations of the original function: 1049 Total number dense interval constraint evaluations: 206330 Total number dense interval constraint gradient component evaluations: 517920 Total number dense point constraint gradient component evaluations: 42200 Total number dense interval reduced gradient evaluations: 12951 Total number of calls to FRITZ_JOHN_RESIDUALS: 3360 Number of times a box was rejected because of a large lower bound on the objective function: 2 Number of times a box was rejected because the gradient or reduced gradient did not contain zero: 131 Average number of overall loop iterations in each call to the reduced interval Newton method): 4.20 Number of times a box was rejected in the interval Newton method due to an empty intersection: 165 Number of times the interval Newton method made a coordinate interval smaller: 5363 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 1289 Number of times a pivoting preconditioner was successful after the first sweep: 1141 Number of times a midpoint matrix was factored: 2006 Total number of times the reduced interval Newton method was tried: 749 Number of times an inverse midpoint preconditioner led to improvement or rejection: 3246 Number of times a C LP preconditioner led to improvement or rejection: 669 N_C_LP_INFEASIBLE = 58 N_LPF_INF_OR_UNB = 58 Number of possible splits as detected by the pivoting preconditioner: 2991 Total time spent in the LP filter (creating and solving the LP): 4.11 Total time spent in subsit (constraint propagation): 0.360E-01 Total time spent in reduced_interval_Newton (iteration to reduce the box): 0.944 Total time spent searching for "D" in the LP filter: 1.06 Total time spent actually solving the linear relaxations: 2.45 Total time spent doing linear algebra (preconditioners and solution processes): 0.596 LIST_BOOKKEEPING_TIME: 0.360E-01 FUNCTION_EVALUATION_TIME (in forward_substitution): 0.200 Time spent setting up pivoting preconditioners: 0.640E-01 Time spent computing pivoting preconditioners: 0.104 Time spent computing LP preconditioners: 0.440E-01 Time spent computing inverse midpoint preconditioners: 0.360E-01 Number of times MAXIT was exceeded in C_LP_DENSE: 8 Number of times the approximate solver was called: 81 Number Fritz-John matrix evaluations: 3234 Number of times SUBSIT decreased one or more coordinate widths: 110 Number times a box was rejected due infeasible inequality constraints: 21 Total number of boxes processed in loop: 752 BEST_ESTIMATE: 975. Overall CPU time: 6.45 CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 0.944 =================================================== =================================================== 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: [ 193. , 194. ], [ 179. , 180. ] [ 185. , 185. ], [ 169. , 169. ] Rigorously verified bounds on the optimum, provided an optimum exists: [ 726. , 727. ]