Output from FIND_GLOBAL_MIN on 05/05/2012 at 03:43:51. Version for the system is: March 13, 2009 Codelist file name is: ex7_2_2G.CDL Box data file name is: ex7_2_2.DT1 Initial box: [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.100E-04, 16.0 ], [ 0.100E-04, 16.0 ] BOUND_CONSTRAINT: 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. LIST OF BOXES CONTAINING VERIFIED FEASIBLE POINTS: Box no.: 1 Box coordinates: [ 0.771 , 0.773 ], [ 0.516 , 0.518 ] [ 0.203 , 0.205 ], [ 0.388 , 0.390 ] [ 3.03 , 3.04 ], [ 5.09 , 5.10 ] PHI: [ -0.390 , -0.388 ] Box contains the following approximate root: 0.772 , 0.517 , 0.204 , 0.389 , 3.04 , 5.10 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ -0.389 , -0.389 ] 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 ] Fritz John multipliers V: [ -1.00 , 1.00 ], [ -1.00 , 1.00 ] [ -1.00 , 1.00 ], [ -1.00 , 1.00 ] INEQ_CERT_FEASIBLE: F F F F F F F F F F F F F NIN_POSS_BINDING: 13 ------------------------------------------------- ALGORITHM COMPLETED WITH LESS THAN THE MAXIMUM NUMBER, 500000 OF BOXES. Number of bisections: 291 No. dense interval residual evaluations -- gradient code list: 6852 Number of orig. system inverse midpoint preconditioner rows: 12409 Number of orig. system C-LP preconditioner rows: 3506 Number of solutions for a component in the expanded system: 47938 Total number of forward_substitutions: 25720 Number of Gauss--Seidel steps on the dense system: 16247 Number point dense residual evaluations, gradient codelist: 786 Number of gradient evaluations from a gradient code list: 2057 Total number of dense slope matrix evaluations: 13796 Total number second-order interval evaluations of the original function: 806 Total number dense interval constraint evaluations: 217334 Total number dense interval constraint gradient component evaluations: 860892 Total number dense point constraint gradient component evaluations: 80172 Total number dense interval reduced gradient evaluations: 8486 Total number of calls to FRITZ_JOHN_RESIDUALS: 2177 Number of times a box was rejected because the constraints were not satisfied: 11 Number of times a box was rejected because the gradient or reduced gradient did not contain zero: 12 Number of times feasible point was found based on the LP_FILTER approximate solution: 3 Average number of overall loop iterations in each call to the reduced interval Newton method): 4.15 Number of times a box was rejected in the interval Newton method due to an empty intersection: 159 Number of times the interval Newton method made a coordinate interval smaller: 6320 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 1359 Number of times a pivoting preconditioner was successful after the first sweep: 853 Number of times a midpoint matrix was factored: 1089 Total number of times the reduced interval Newton method was tried: 482 Number of times an inverse midpoint preconditioner led to improvement or rejection: 1915 Number of times a C LP preconditioner led to improvement or rejection: 1004 N_C_LP_INFEASIBLE = 265 N_NEW_BEST_ESTIMATE_WITH_LP filter = 3 N_LPF_INF_OR_UNB = 265 Number of possible splits as detected by the pivoting preconditioner: 1967 Total time spent in the LP filter (creating and solving the LP): 1.18 Total time spent in subsit (constraint propagation): 0.320E-01 Total time spent in reduced_interval_Newton (iteration to reduce the box): 1.14 Total time spent actually solving the linear relaxations: 1.08 Total time spent doing linear algebra (preconditioners and solution processes): 0.728 LIST_BOOKKEEPING_TIME: 0.800E-02 FUNCTION_EVALUATION_TIME (in forward_substitution): 0.272 Time spent setting up pivoting preconditioners: 0.800E-01 Time spent computing pivoting preconditioners: 0.760E-01 Time spent computing LP preconditioners: 0.440E-01 Time spent computing inverse midpoint preconditioners: 0.160E-01 Number of times MAXIT was exceeded in C_LP_DENSE: 3 Number of unbounded problems found in C_LP_DENSE: 1 Number Fritz-John matrix evaluations: 2165 Number of times SUBSIT decreased one or more coordinate widths: 184 Number of times SUBSIT rejected a box: 23 Number times a box was rejected due infeasible inequality constraints: 9 Total number of boxes processed in loop: 508 N_FINDOPT_SUCCESS = 66 BEST_ESTIMATE: -0.389 Overall CPU time: 3.91 CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 1.14 =================================================== =================================================== Number of boxes in the list with proven feasible points: 1 Number of boxes in the list of other small boxes: 0 Number of unfathomed boxes: 0 Interval hull of the boxes verified to contain feasible points or critical points: [ 0.771 , 0.773 ], [ 0.516 , 0.518 ] [ 0.203 , 0.205 ], [ 0.388 , 0.390 ] [ 3.03 , 3.04 ], [ 5.09 , 5.10 ] Rigorously verified bounds on the optimum, provided an optimum exists: [ -0.390 , -0.389 ]