Output from FIND_GLOBAL_MIN on 05/08/2012 at 00:45:13. Version for the system is: March 13, 2009 Codelist file name is: ex6_2_12G.CDL Box data file name is: ex6_2_12.DT1 Initial box: [ 0.100E-06, 0.500 ], [ 0.100E-06, 0.500 ] [ 0.100E-06, 0.500 ], [ 0.100E-06, 0.500 ] BOUND_CONSTRAINT: 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: [ 0.100E-06, 0.158E-02 ], [ 0.498 , 0.500 ] [ 0.381 , 0.383 ], [ 0.117 , 0.119 ] PHI: [ -0.295E-01, 0.593 ] Box contains the following approximate root: 0.791E-03, 0.499 , 0.382 , 0.118 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 0.289 , 0.289 ] 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 ] Fritz John multipliers V: [ -1.00 , 1.00 ], [ -1.00 , 1.00 ] INEQ_CERT_FEASIBLE: F F F F F F F F NIN_POSS_BINDING: 8 ------------------------------------------------- Box no.: 2 Box coordinates: [ 0.498 , 0.500 ], [ 0.100E-06, 0.158E-02 ] [ 0.117 , 0.119 ], [ 0.381 , 0.383 ] PHI: [ -0.295E-01, 0.593 ] Box contains the following approximate root: 0.499 , 0.791E-03, 0.118 , 0.382 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 0.289 , 0.289 ] 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 ] Fritz John multipliers V: [ -1.00 , 1.00 ], [ -1.00 , 1.00 ] INEQ_CERT_FEASIBLE: F F F F F F F F NIN_POSS_BINDING: 8 ------------------------------------------------- ALGORITHM COMPLETED WITH LESS THAN THE MAXIMUM NUMBER, 500000 OF BOXES. Number of bisections: 4205 No. dense interval residual evaluations -- gradient code list: 78198 Number of orig. system inverse midpoint preconditioner rows: 86275 Number of orig. system C-LP preconditioner rows: 30986 Number of solutions for a component in the expanded system: 1299682 Total number of forward_substitutions: 277726 Number of Gauss--Seidel steps on the dense system: 127636 Number point dense residual evaluations, gradient codelist: 4124 Number of gradient evaluations from a gradient code list: 23787 Total number of dense slope matrix evaluations: 94628 Total number second-order interval evaluations of the original function: 13596 Total number dense interval constraint evaluations: 1013024 Total number dense interval constraint gradient component evaluations: 2250640 Total number dense point constraint gradient component evaluations: 170800 Total number dense interval reduced gradient evaluations: 80399 Total number of calls to FRITZ_JOHN_RESIDUALS: 20313 Number of times a box was rejected because of a large lower bound on the objective function: 3 Number of times a box was rejected because the gradient or reduced gradient did not contain zero: 55 Number of times feasible point was found based on the LP_FILTER approximate solution: 6 Average number of overall loop iterations in each call to the reduced interval Newton method): 3.82 Number of times a box was rejected in the interval Newton method due to an empty intersection: 856 Number of times the interval Newton method made a coordinate interval smaller: 29621 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 8982 Number of times a pivoting preconditioner was successful after the first sweep: 2956 Number of times a midpoint matrix was factored: 12347 Total number of times the reduced interval Newton method was tried: 5119 Number of times an inverse midpoint preconditioner led to improvement or rejection: 14391 Number of times a C LP preconditioner led to improvement or rejection: 2655 Number of times computing a C_LP failed 326 N_C_LP_INFEASIBLE = 15 N_NEW_BEST_ESTIMATE_WITH_LP filter = 6 N_LPF_INF_OR_UNB = 15 Number of possible splits as detected by the pivoting preconditioner: 19515 Total time spent in the LP filter (creating and solving the LP): 34.5 Total time spent in subsit (constraint propagation): 1.39 Total time spent in reduced_interval_Newton (iteration to reduce the box): 20.2 Total time spent searching for "D" in the LP filter: 0.280 Total time spent actually solving the linear relaxations: 27.5 Total time spent doing linear algebra (preconditioners and solution processes): 2.46 LIST_BOOKKEEPING_TIME: 1.33 FUNCTION_EVALUATION_TIME (in forward_substitution): 39.4 Time spent setting up pivoting preconditioners: 0.336 Time spent computing pivoting preconditioners: 0.308 Time spent computing LP preconditioners: 0.316 Time spent computing inverse midpoint preconditioners: 0.200 Number of times MAXIT was exceeded in C_LP_DENSE: 61 Number of unbounded problems found in C_LP_DENSE: 326 Number of times the approximate solver was called: 1 Number Fritz-John matrix evaluations: 20258 Number of times SUBSIT decreased one or more coordinate widths: 1242 Number of times SUBSIT rejected a box: 8 Total number of boxes processed in loop: 5133 N_FINDOPT_SUCCESS = 248 BEST_ESTIMATE: 0.289 Overall CPU time: 104. CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 20.2 =================================================== =================================================== Number of boxes in the list with proven feasible points: 2 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: [ 0.100E-06, 0.500 ], [ 0.100E-06, 0.500 ] [ 0.117 , 0.383 ], [ 0.117 , 0.383 ] Rigorously verified bounds on the optimum, provided an optimum exists: [ -0.295E-01, 0.289 ]