Output from FIND_GLOBAL_MIN on 05/02/2012 at 16:36:03. Version for the system is: March 13, 2009 Codelist file name is: immunG.CDL Box data file name is: immun.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 ] [ -0.100E+05, 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 ] [ 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 F F 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: 76308 Number of bisections: 76456 No. dense interval residual evaluations -- gradient code list: 1886010 Number of orig. system inverse midpoint preconditioner rows: 273886 Number of orig. system C-LP preconditioner rows: 2172162 Number of solutions for a component in the expanded system: 14336233 Total number of forward_substitutions: 11670459 Number of Gauss--Seidel steps on the dense system: 25414555 Number point dense residual evaluations, gradient codelist: 30 Number of gradient evaluations from a gradient code list: 382719 Total number of dense slope matrix evaluations: 20473688 Total number second-order interval evaluations of the original function: 152912 Total number dense interval constraint evaluations: 126785575 Total number dense interval constraint gradient component evaluations: 1931983956 Total number dense point constraint gradient component evaluations: 132888 Total number dense interval reduced gradient evaluations: 3870624 Total number of calls to FRITZ_JOHN_RESIDUALS: 967656 Average number of overall loop iterations in each call to the reduced interval Newton method): 12.6 Number of times a box was rejected in the interval Newton method due to an empty intersection: 145 Number of times the interval Newton method made a coordinate interval smaller: 1697454 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 142410 Number of times a pivoting preconditioner was successful after the first sweep: 115388 Number of times a midpoint matrix was factored: 883656 Total number of times the reduced interval Newton method was tried: 76601 Number of times an inverse midpoint preconditioner led to improvement or rejection: 19 Number of times a C LP preconditioner led to improvement or rejection: 1555170 Number of times computing a C_LP failed 1402 N_C_LP_INFEASIBLE = 268 N_LPF_INF_OR_UNB = 268 Number of possible splits as detected by the pivoting preconditioner: 967656 Total time spent in the LP filter (creating and solving the LP): 669. Total time spent in subsit (constraint propagation): 7.09 Total time spent in reduced_interval_Newton (iteration to reduce the box): 0.594E+04 Total time spent searching for "D" in the LP filter: 53.4 Total time spent actually solving the linear relaxations: 553. Total time spent doing linear algebra (preconditioners and solution processes): 0.407E+04 Total time spent running the approximate optimizer: 0.120E-01 LIST_BOOKKEEPING_TIME: 397. FUNCTION_EVALUATION_TIME (in forward_substitution): 160. Time spent setting up pivoting preconditioners: 370. Time spent computing pivoting preconditioners: 137. Time spent computing LP preconditioners: 0.108E+04 Time spent computing inverse midpoint preconditioners: 210. Number of times MAXIT was exceeded in C_LP_DENSE: 2797 Number of unbounded problems found in C_LP_DENSE: 1402 Number of times the approximate solver was called: 1 Number Fritz-John matrix evaluations: 967656 Number of times SUBSIT decreased one or more coordinate widths: 26235 Number of times SUBSIT rejected a box: 4 Number times a box was rejected due infeasible inequality constraints: 1 Total number of boxes processed in loop: 76605 BEST_ESTIMATE: 0.959E+10 Overall CPU time: 0.720E+04 CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 0.594E+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: 76308 Interval hull of the unfathomed boxes: [ 0.00 , 0.223-307 ], [ 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 ] [ -0.178-306, 0.100E+05 ], [ 0.00 , 19.1 ] [ 0.00 , 18.5 ], [ 0.00 , 17.1 ] [ 0.00 , 17.9 ], [ 0.00 , 17.8 ] [ 0.00 , 149. ], [ 0.00 , 147. ] [ 0.00 , 108. ], [ 0.00 , 0.223-307 ] [ 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 ] Rigorously verified bounds on the optimum, provided an optimum exists: [ 0.565E+10, 0.949E+10 ] FIRST UNFINISHED BOX: Box coordinates: [ 0.00 , 0.223-307 ], [ 0.100E+05, 0.100E+05 ] [ 0.100E+05, 0.100E+05 ], [ 0.100E+05, 0.100E+05 ] [ 0.100E+05, 0.100E+05 ], [ 0.100E+05, 0.100E+05 ] [ 0.465E+04, 0.532E+04 ], [ 7.99 , 11.3 ] [ 3.17 , 6.33 ], [ 0.00 , 1.10 ] [ 0.00 , 4.48 ], [ 0.00 , 2.22 ] [ 18.6 , 27.9 ], [ 18.3 , 27.5 ] [ 54.0 , 64.0 ], [ 0.00 , 0.223-307 ] [ 0.802E+04, 0.100E+05 ], [ 0.412E+04, 0.552E+04 ] [ 0.00 , 762. ], [ 0.00 , 0.116E+04 ] [ 0.500E+04, 0.100E+05 ] PHI: [ 0.565E+10, 0.565E+10 ] Box does not contain an approximate root. Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.00 , 0.173E-16 ] Fritz John multipliers U: [ 0.414 , 0.414 ], [ 0.00 , 1.00 ] [ 0.00 , 0.309E-12 ], [ 0.00 , 0.183E-12 ] [ 0.00 , 0.174E-12 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 0.920E-11 ] [ 0.00 , 0.496E-10 ], [ 0.00 , 0.678E-12 ] [ 0.00 , 0.203E-10 ], [ 0.00 , 0.222E-10 ] [ 0.00 , 0.229E-10 ], [ 0.00 , 0.461E-10 ] [ 0.00 , 0.315E-10 ], [ 0.414 , 0.414 ] [ 0.00 , 0.660E-16 ], [ 0.00 , 0.954E-16 ] [ 0.00 , 0.136E-12 ], [ 0.00 , 0.876E-14 ] [ 0.00 , 0.493E-16 ] Fritz John multipliers V: [ -0.414 , -0.414 ], [ -0.138E-16, 0.182E-16 ] [ -0.287E-15, 0.175E-16 ], [ -0.287E-15, 0.171E-16 ] [ -0.441E-16, 0.163E-16 ], [ -0.606E-16, 0.932E-17 ] [ -0.347-301, 0.347-301 ] INEQ_CERT_FEASIBLE: F T T T T T T T T F F F T T T F T T F F T NIN_POSS_BINDING: 7 LAST UNFINISHED BOX: Box coordinates: [ 0.00 , 0.223-307 ], [ 0.00 , 0.500E+04 ] [ 0.00 , 0.100E+05 ], [ 0.00 , 0.100E+05 ] [ 0.00 , 0.100E+05 ], [ 0.00 , 0.100E+05 ] [ -0.178-306, 0.100E+05 ], [ 0.00 , 19.1 ] [ 0.00 , 18.5 ], [ 0.00 , 17.1 ] [ 0.00 , 17.9 ], [ 0.00 , 17.8 ] [ 0.00 , 149. ], [ 0.00 , 147. ] [ 0.00 , 108. ], [ 0.00 , 0.223-307 ] [ 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 ] PHI: [ 0.607E+10, 0.949E+10 ] Box does not contain an approximate root. Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.00 , 0.361 ] 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 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 0.928E-02 ], [ 0.00 , 0.808E-01 ] [ 0.00 , 0.452E-01 ], [ 0.00 , 0.311E-02 ] [ 0.00 , 0.283E-02 ] Fritz John multipliers V: [ -1.00 , 0.824E-13 ], [ -0.134E-02, 0.111E-14 ] [ -0.196E-02, 0.101E-14 ], [ -0.424E-01, 0.226E-15 ] [ -0.139E-02, 0.413E-16 ], [ -0.283E-02, 0.932E-17 ] [ -0.347-301, 0.347-301 ] INEQ_CERT_FEASIBLE: F F F F F F T F F F F F F F F F F F F F F NIN_POSS_BINDING: 20 Total volume of the boxes that have not yet been processed: 0.0000000000000000