Output from FIND_GLOBAL_MIN on 05/07/2012 at 13:43:56. Version for the system is: March 13, 2009 Codelist file name is: ex3_1_2G.CDL Box data file name is: ex3_1_2.DT1 Initial box: [ 78.0 , 102. ], [ 27.0 , 45.0 ] [ 27.0 , 45.0 ], [ 33.0 , 45.0 ] [ 27.0 , 45.0 ] 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: [ 78.0 , 78.1 ], [ 30.0 , 30.0 ] [ 36.7 , 36.8 ], [ 33.0 , 33.0 ] [ 44.9 , 45.0 ] PHI: [ -0.307E+05, -0.306E+05 ] Box contains the following approximate root: 78.0 , 30.0 , 36.8 , 33.0 , 45.0 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ -0.307E+05, -0.307E+05 ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.728E-03, 0.728E-03 ] Fritz John multipliers U: [ 0.294 , 0.294 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.589 , 0.589 ] [ 0.356E-01, 0.356E-01 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.614E-01, 0.614E-01 ], [ 0.00 , 0.126E-01 ] [ 0.00 , 0.437 ], [ 0.194E-01, 0.194E-01 ] INEQ_CERT_FEASIBLE: F T T T T F F T T T T T F T T F NIN_POSS_BINDING: 5 ------------------------------------------------- LIST OF BOXES CONTAINING VERIFIED FEASIBLE POINTS: Box no.: 1 Box coordinates: [ 86.1 , 86.3 ], [ 33.7 , 33.7 ] [ 32.3 , 32.3 ], [ 39.6 , 39.7 ] [ 32.9 , 33.0 ] PHI: [ -0.292E+05, -0.291E+05 ] Box contains the following approximate root: 86.2 , 33.7 , 32.3 , 39.7 , 32.9 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ -0.292E+05, -0.292E+05 ] 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 ], [ 0.00 , 1.00 ] INEQ_CERT_FEASIBLE: F F F F F F F F F F F F F F F F NIN_POSS_BINDING: 16 ------------------------------------------------- ALGORITHM COMPLETED WITH LESS THAN THE MAXIMUM NUMBER, 500000 OF BOXES. Number of bisections: 53 No. dense interval residual evaluations -- gradient code list: 6729 Number of orig. system inverse midpoint preconditioner rows: 3750 Number of orig. system C-LP preconditioner rows: 317 Number of solutions for a component in the expanded system: 23223 Total number of forward_substitutions: 25678 Number of Gauss--Seidel steps on the dense system: 4761 Number point dense residual evaluations, gradient codelist: 35 Number of gradient evaluations from a gradient code list: 438 Total number of dense slope matrix evaluations: 28348 Total number second-order interval evaluations of the original function: 148 Total number dense interval constraint evaluations: 378256 Total number dense interval constraint gradient component evaluations: 1389840 Total number dense point constraint gradient component evaluations: 4720 Total number dense interval reduced gradient evaluations: 22578 Total number of calls to FRITZ_JOHN_RESIDUALS: 5649 Number of times a box was rejected because the gradient or reduced gradient did not contain zero: 8 Average number of overall loop iterations in each call to the reduced interval Newton method): 51.8 Number of times a box was rejected in the interval Newton method due to an empty intersection: 46 Number of times the interval Newton method made a coordinate interval smaller: 6788 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 5840 Number of times a pivoting preconditioner was successful after the first sweep: 5834 Number of times a midpoint matrix was factored: 319 Total number of times the reduced interval Newton method was tried: 109 Number of times an inverse midpoint preconditioner led to improvement or rejection: 656 Number of times a C LP preconditioner led to improvement or rejection: 338 N_C_LP_INFEASIBLE = 3 N_LPF_INF_OR_UNB = 3 Number of possible splits as detected by the pivoting preconditioner: 5640 Total time spent in the LP filter (creating and solving the LP): 0.528 Total time spent in subsit (constraint propagation): 0.200E-01 Total time spent in reduced_interval_Newton (iteration to reduce the box): 1.72 Total time spent searching for "D" in the LP filter: 0.112 Total time spent actually solving the linear relaxations: 0.344 Total time spent doing linear algebra (preconditioners and solution processes): 0.628 LIST_BOOKKEEPING_TIME: 0.120E-01 FUNCTION_EVALUATION_TIME (in forward_substitution): 0.248 Time spent setting up pivoting preconditioners: 0.228 Time spent computing pivoting preconditioners: 0.244 Time spent computing LP preconditioners: 0.200E-01 Time spent computing inverse midpoint preconditioners: 0.200E-01 Number of times MAXIT was exceeded in C_LP_DENSE: 4 Number of times the approximate solver was called: 3 Number Fritz-John matrix evaluations: 5640 Number of times SUBSIT decreased one or more coordinate widths: 82 Number of times SUBSIT rejected a box: 5 Number times a box was rejected due infeasible inequality constraints: 4 Total number of boxes processed in loop: 114 N_FINDOPT_SUCCESS = 2 BEST_ESTIMATE: -0.292E+05 Overall CPU time: 2.38 CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 1.72 =================================================== =================================================== 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: 0 Interval hull of the boxes verified to contain feasible points or critical points: [ 86.1 , 86.3 ], [ 33.7 , 33.7 ] [ 32.3 , 32.3 ], [ 39.6 , 39.7 ] [ 32.9 , 33.0 ] Interval hull of the small unverified boxes: [ 78.0 , 78.1 ], [ 30.0 , 30.0 ] [ 36.7 , 36.8 ], [ 33.0 , 33.0 ] [ 44.9 , 45.0 ] Rigorously verified bounds on the optimum, provided an optimum exists: [ -0.307E+05, -0.292E+05 ]