Output from FIND_GLOBAL_MIN on 05/07/2012 at 20:41:05. Version for the system is: March 13, 2009 Codelist file name is: ex14_2_4_sourceG.CDL Box data file name is: ex14_2_4_source.DT1 Initial box: [ 0.100E-05, 1.00 ], [ 0.100E-05, 1.00 ] [ 0.100E-05, 1.00 ], [ 40.0 , 90.0 ] [ 0.00 , 0.100E+05 ] BOUND_CONSTRAINT: 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: [ 0.186 , 0.188 ], [ 0.559 , 0.561 ] [ 0.251 , 0.253 ], [ 72.9 , 73.0 ] [ 0.00 , 0.150E-02 ] PHI: [ 0.00 , 0.150E-02 ] Box contains the following approximate root: 0.187 , 0.560 , 0.252 , 73.0 , -0.994E-08 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ -0.994E-08, -0.994E-08 ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.500 , 0.500 ] Fritz John multipliers U: [ 0.00 , 0.286 ], [ 0.00 , 0.405 ] [ 0.00 , 0.412 ], [ 0.00 , 0.286 ] [ 0.00 , 0.405 ], [ 0.00 , 0.414 ] [ 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 , 0.157 ], [ 0.00 , 0.125 ] [ 0.00 , 0.519 ] Fritz John multipliers V: [ -0.294E-06, 0.294E-06 ] INEQ_CERT_FEASIBLE: F F F F F F T T T T T T T T F NIN_POSS_BINDING: 7 ------------------------------------------------- LIST OF BOXES CONTAINING VERIFIED FEASIBLE POINTS: Box no.: 1 Box coordinates: [ 0.332 , 0.334 ], [ 0.332 , 0.334 ] [ 0.332 , 0.334 ], [ 72.6 , 72.7 ] [ 0.347E+04, 0.348E+04 ] PHI: [ 0.347E+04, 0.348E+04 ] Box contains the following approximate root: 0.333 , 0.333 , 0.333 , 72.6 , 0.348E+04 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 0.348E+04, 0.348E+04 ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.00 , 1.00 ] 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 ] Fritz John multipliers V: [ -1.00 , 1.00 ] INEQ_CERT_FEASIBLE: F F F F F F F F F F F F F F F NIN_POSS_BINDING: 15 ------------------------------------------------- ALGORITHM COULD NOT COMPLETE WITH LESS THAN 500000 BOXES CONSIDERED. Number of boxes that have not yet been processed: 12801 Number of bisections: 357533 No. dense interval residual evaluations -- gradient code list: 6226691 Number of orig. system inverse midpoint preconditioner rows: 12662195 Number of orig. system C-LP preconditioner rows: 2361685 Number of solutions for a component in the expanded system: 21930159 Total number of forward_substitutions: 20071270 Number of Gauss--Seidel steps on the dense system: 15097392 Number point dense residual evaluations, gradient codelist: 81065 Number of gradient evaluations from a gradient code list: 2196454 Total number of dense slope matrix evaluations: 6699434 Total number second-order interval evaluations of the original function: 759949 Total number dense interval constraint evaluations: 160098367 Total number dense interval constraint gradient component evaluations: 462331880 Total number dense point constraint gradient component evaluations: 8659920 Total number dense interval reduced gradient evaluations: 4787896 Total number of calls to FRITZ_JOHN_RESIDUALS: 1206051 Number of times a box was rejected because the gradient or reduced gradient did not contain zero: 18141 Number of times a box was rejected due to infeasibility in LP_FILTER: 316 Average number of overall loop iterations in each call to the reduced interval Newton method): 2.58 Number of times a box was rejected in the interval Newton method due to an empty intersection: 57381 Number of times the interval Newton method made a coordinate interval smaller: 1344161 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 273060 Number of times a pivoting preconditioner was successful after the first sweep: 16725 Number of times a midpoint matrix was factored: 1003956 Total number of times the reduced interval Newton method was tried: 490510 Number of times an inverse midpoint preconditioner led to improvement or rejection: 978501 Number of times a C LP preconditioner led to improvement or rejection: 149981 Number of times computing a C_LP failed 15425 N_C_LP_INFEASIBLE = 452894 N_C_LP_GENERAL_FAILURE = 2 N_LP_FILTER_FAILURE = 1 N_REJECT_WITH_LP filter = 367 N_LPF_INF_OR_UNB = 452794 Number of possible splits as detected by the pivoting preconditioner: 1187897 Total time spent in the LP filter (creating and solving the LP): 0.376E+04 Total time spent in subsit (constraint propagation): 28.2 Total time spent in reduced_interval_Newton (iteration to reduce the box): 0.133E+04 Total time spent searching for "D" in the LP filter: 13.3 Total time spent actually solving the linear relaxations: 0.343E+04 Total time spent doing linear algebra (preconditioners and solution processes): 607. Total time spent running the approximate optimizer: 1.27 LIST_BOOKKEEPING_TIME: 281. FUNCTION_EVALUATION_TIME (in forward_substitution): 630. Time spent setting up pivoting preconditioners: 51.4 Time spent computing pivoting preconditioners: 65.5 Time spent computing LP preconditioners: 71.5 Time spent computing inverse midpoint preconditioners: 40.7 Number of times MAXIT was exceeded in C_LP_DENSE: 279 Number of unbounded problems found in C_LP_DENSE: 15425 Number of times the approximate solver was called: 6796 Number Fritz-John matrix evaluations: 1187897 Number of times SUBSIT decreased one or more coordinate widths: 2140 Number of times SUBSIT rejected a box: 9122 Number times a box was rejected due infeasible inequality constraints: 64251 Total number of boxes processed in loop: 500000 N_FINDOPT_SUCCESS = 6795 BEST_ESTIMATE: 0.348E+04 Overall CPU time: 0.623E+04 CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 0.133E+04 =================================================== =================================================== Number of boxes in the list with proven feasible points: 1 Number of boxes in the list of other small boxes: 1 Number of unfathomed boxes: 12801 Interval hull of the boxes verified to contain feasible points or critical points: [ 0.332 , 0.334 ], [ 0.332 , 0.334 ] [ 0.332 , 0.334 ], [ 72.6 , 72.7 ] [ 0.347E+04, 0.348E+04 ] Interval hull of the small unverified boxes: [ 0.186 , 0.188 ], [ 0.559 , 0.561 ] [ 0.251 , 0.253 ], [ 72.9 , 73.0 ] [ 0.00 , 0.150E-02 ] Interval hull of the unfathomed boxes: [ 0.100E-05, 1.00 ], [ 0.100E-05, 1.00 ] [ 0.100E-05, 1.00 ], [ 40.0 , 90.0 ] [ 0.179E-02, 0.500E+04 ] Rigorously verified bounds on the optimum, provided an optimum exists: [ 0.00 , 0.348E+04 ] FIRST UNFINISHED BOX: Box coordinates: [ 0.184 , 0.185 ], [ 0.563 , 0.563 ] [ 0.252 , 0.253 ], [ 72.9 , 72.9 ] [ 0.179E-02, 0.209E-02 ] PHI: [ 0.179E-02, 0.209E-02 ] Box does not contain an approximate root. Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.500 , 0.500 ] Fritz John multipliers U: [ 0.00 , 0.250 ], [ 0.00 , 0.354 ] [ 0.00 , 0.250 ], [ 0.00 , 0.250 ] [ 0.00 , 0.699E-02 ], [ 0.00 , 0.255 ] [ 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 , 0.157 ], [ 0.00 , 0.125 ] [ 0.00 , 0.504 ] Fritz John multipliers V: [ -0.451E-02, 0.451E-02 ] INEQ_CERT_FEASIBLE: F T F F F F T T T T T T T T T NIN_POSS_BINDING: 5 LAST UNFINISHED BOX: Box coordinates: [ 0.100E-05, 0.332 ], [ 0.250 , 0.500 ] [ 0.168 , 0.750 ], [ 40.0 , 90.0 ] [ 0.250E+04, 0.500E+04 ] PHI: [ 0.250E+04, 0.500E+04 ] Box does not contain an approximate root. Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.00 , 1.00 ] 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 , 0.157 ], [ 0.00 , 0.157 ] [ 0.00 , 1.00 ] Fritz John multipliers V: [ -1.00 , 1.00 ] INEQ_CERT_FEASIBLE: F F F F F F F T T T T T F F F NIN_POSS_BINDING: 10 Total volume of the boxes that have not yet been processed: 117597.24153582280