Output from FIND_GLOBAL_MIN on 05/04/2012 at 22:00:37. Version for the system is: March 13, 2009 Codelist file name is: ex14_1_4G.CDL Box data file name is: ex14_1_4.DT1 Initial box: [ 0.250 , 1.00 ], [ 1.50 , 6.28 ] [ -0.100E+05, 0.100E+05 ] BOUND_CONSTRAINT: 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: [ 0.298 , 0.300 ], [ 2.83 , 2.84 ] [ -0.100E-02, 0.100E-02 ] PHI: [ -0.100E-02, 0.100E-02 ] Box contains the following approximate root: 0.500 , 3.14 , -0.996E-08 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ -0.996E-08, -0.996E-08 ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.500 , 0.500 ] Fritz John multipliers U: [ 0.00 , 0.259 ], [ 0.00 , 0.251 ] [ 0.00 , 0.259 ], [ 0.00 , 0.251 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 0.695 ], [ 0.00 , 1.00 ] INEQ_CERT_FEASIBLE: F F F F T T T T NIN_POSS_BINDING: 4 ------------------------------------------------- Box no.: 2 Box coordinates: [ 0.499 , 0.501 ], [ 3.14 , 3.14 ] [ -0.100E-02, 0.100E-02 ] PHI: [ -0.100E-02, 0.100E-02 ] Box contains the following approximate root: 0.500 , 3.14 , -0.996E-08 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ -0.996E-08, -0.996E-08 ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.500 , 0.500 ] Fritz John multipliers U: [ 0.00 , 0.255 ], [ 0.00 , 0.252 ] [ 0.00 , 0.255 ], [ 0.00 , 0.252 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 0.695 ], [ 0.00 , 1.00 ] INEQ_CERT_FEASIBLE: F F F F T T T T NIN_POSS_BINDING: 4 ------------------------------------------------- Box no.: 3 Box coordinates: [ 0.399 , 0.401 ], [ 3.06 , 3.07 ] [ 0.256E-01, 0.276E-01 ] PHI: [ 0.256E-01, 0.276E-01 ] Box contains the following approximate root: 0.500 , 3.14 , -0.996E-08 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ -0.996E-08, -0.996E-08 ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.500 , 0.500 ] Fritz John multipliers U: [ 0.493 , 0.493 ], [ 0.685E-02, 0.685E-02 ] [ 0.00 , 0.500 ], [ 0.00 , 0.255 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 0.695 ], [ 0.00 , 1.00 ] INEQ_CERT_FEASIBLE: F F 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: 3193 No. dense interval residual evaluations -- gradient code list: 49240 Number of orig. system inverse midpoint preconditioner rows: 33687 Number of orig. system C-LP preconditioner rows: 27159 Number of solutions for a component in the expanded system: 162150 Total number of forward_substitutions: 142938 Number of Gauss--Seidel steps on the dense system: 61533 Number point dense residual evaluations, gradient codelist: 10787 Number of gradient evaluations from a gradient code list: 18226 Total number of dense slope matrix evaluations: 29687 Total number second-order interval evaluations of the original function: 7823 Total number dense interval constraint evaluations: 600896 Total number dense interval constraint gradient component evaluations: 966000 Total number dense point constraint gradient component evaluations: 280320 Total number dense interval reduced gradient evaluations: 28518 Total number of calls to FRITZ_JOHN_RESIDUALS: 7448 Number of times a box was rejected because the gradient or reduced gradient did not contain zero: 159 Number of times a box was rejected due to infeasibility in LP_FILTER: 10 Number of times feasible point was found based on the LP_FILTER approximate solution: 1 Average number of overall loop iterations in each call to the reduced interval Newton method): 1.70 Number of times a box was rejected in the interval Newton method due to an empty intersection: 1334 Number of times the interval Newton method made a coordinate interval smaller: 7961 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 2727 Number of times a pivoting preconditioner was successful after the first sweep: 2174 Number of times a midpoint matrix was factored: 4433 Total number of times the reduced interval Newton method was tried: 3900 Number of times an inverse midpoint preconditioner led to improvement or rejection: 3101 Number of times a C LP preconditioner led to improvement or rejection: 585 Number of times computing a C_LP failed 1 N_C_LP_INFEASIBLE = 1730 N_NEW_BEST_ESTIMATE_WITH_LP filter = 1 N_REJECT_WITH_LP filter = 27 N_LPF_INF_OR_UNB = 1728 Number of times a C LP preconditioner was not computed because the heuristic determined it was not worth it: 1173 Number of possible splits as detected by the pivoting preconditioner: 6334 Total time spent in the LP filter (creating and solving the LP): 9.29 Total time spent in subsit (constraint propagation): 0.148 Total time spent in reduced_interval_Newton (iteration to reduce the box): 2.92 Total time spent searching for "D" in the LP filter: 0.560E-01 Total time spent actually solving the linear relaxations: 8.08 Total time spent doing linear algebra (preconditioners and solution processes): 1.60 Total time spent running the approximate optimizer: 0.120E-01 LIST_BOOKKEEPING_TIME: 0.204 FUNCTION_EVALUATION_TIME (in forward_substitution): 2.10 Time spent setting up pivoting preconditioners: 0.120 Time spent computing pivoting preconditioners: 0.152 Time spent computing LP preconditioners: 0.316 Time spent computing inverse midpoint preconditioners: 0.800E-01 Number of times MAXIT was exceeded in C_LP_DENSE: 1 Number of unbounded problems found in C_LP_DENSE: 1 Number of times the approximate solver was called: 942 Number Fritz-John matrix evaluations: 7288 Number of times SUBSIT decreased one or more coordinate widths: 171 Number of times SUBSIT rejected a box: 60 Number times a box was rejected due infeasible inequality constraints: 162 Total number of boxes processed in loop: 3997 N_FINDOPT_SUCCESS = 4 BEST_ESTIMATE: 0.357E-01 Overall CPU time: 27.2 CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 2.92 =================================================== =================================================== 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: [ 0.298 , 0.501 ], [ 2.83 , 3.14 ] [ -0.100E-02, 0.276E-01 ] Rigorously verified bounds on the optimum, provided an optimum exists: [ -0.100E-02, 0.276E-01 ]