Output from FIND_GLOBAL_MIN on 05/07/2012 at 08:39:16. Version for the system is: March 13, 2009 Codelist file name is: ex8_4_4G.CDL Box data file name is: ex8_4_4.DT1 Initial box: [ 0.00 , 1.00 ], [ 1.10 , 1.30 ] [ 0.00 , 1.00 ], [ 4.00 , 6.00 ] [ -6.00 , -4.00 ], [ 2.00 , 4.00 ] [ -3.00 , -1.00 ], [ 1.00 , 3.00 ] [ -2.00 , 0.00 ], [ 0.500 , 2.50 ] [ -1.50 , 0.500 ], [ 0.200 , 2.20 ] [ -1.20 , 0.800 ], [ 0.100 , 2.10 ] [ -1.10 , 0.900 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ] 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 --------------------------------------- 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: [ 0.556 , 0.558 ], [ 1.13 , 1.13 ] [ 0.621 , 0.623 ], [ 5.13 , 5.14 ] [ -4.94 , -4.93 ], [ 2.67 , 2.67 ] [ -2.07 , -2.07 ], [ 1.91 , 1.91 ] [ -1.10 , -1.10 ], [ 1.55 , 1.55 ] [ -0.582 , -0.580 ], [ 1.34 , 1.34 ] [ -0.229 , -0.227 ], [ 1.20 , 1.20 ] [ 0.410E-01, 0.430E-01 ], [ 0.605 , 0.607 ] [ 0.749 , 0.751 ] PHI: [ 0.207 , 0.218 ] Box contains the following approximate root: 0.557 , 1.13 , 0.622 , 5.13 , -4.94 , 2.67 -2.07 , 1.91 , -1.10 , 1.55 , -0.581 , 1.34 -0.228 , 1.20 , 0.420E-01, 0.606 , 0.750 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 0.212 , 0.212 ] 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 ] [ 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 , 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 ] [ -1.00 , 1.00 ], [ -1.00 , 1.00 ] [ -1.00 , 1.00 ], [ -1.00 , 1.00 ] [ -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 F F F F F F F F F F F F F F F F F F F F F NIN_POSS_BINDING: 34 ------------------------------------------------- ALGORITHM COMPLETED WITH LESS THAN THE MAXIMUM NUMBER, 500000 OF BOXES. Number of bisections: 12490 No. dense interval residual evaluations -- gradient code list: 315151 Number of orig. system inverse midpoint preconditioner rows: 2437010 Number of orig. system C-LP preconditioner rows: 104998 Number of solutions for a component in the expanded system: 18857798 Total number of forward_substitutions: 1793111 Number of Gauss--Seidel steps on the dense system: 2629614 Number point dense residual evaluations, gradient codelist: 479 Number of gradient evaluations from a gradient code list: 90941 Total number of dense slope matrix evaluations: 1720417 Total number second-order interval evaluations of the original function: 31654 Total number dense interval constraint evaluations: 21288610 Total number dense interval constraint gradient component evaluations: 211187158 Total number dense point constraint gradient component evaluations: 412114 Total number dense interval reduced gradient evaluations: 401402 Total number of calls to FRITZ_JOHN_RESIDUALS: 101434 Number of times a box was rejected because of a large lower bound on the objective function: 79 Number of times a box was rejected because the constraints were not satisfied: 175 Number of times a box was rejected because the gradient or reduced gradient did not contain zero: 2095 Number of times feasible point was found based on the LP_FILTER approximate solution: 2 Average number of overall loop iterations in each call to the reduced interval Newton method): 4.96 Number of times a box was rejected in the interval Newton method due to an empty intersection: 5635 Number of times the interval Newton method made a coordinate interval smaller: 619675 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 27665 Number of times a pivoting preconditioner was successful after the first sweep: 19243 Number of times a midpoint matrix was factored: 85141 Total number of times the reduced interval Newton method was tried: 20474 Number of times an inverse midpoint preconditioner led to improvement or rejection: 539801 Number of times a C LP preconditioner led to improvement or rejection: 53769 Number of times computing a C_LP failed 9 N_C_LP_INFEASIBLE = 18956 N_NEW_BEST_ESTIMATE_WITH_LP filter = 2 N_LPF_INF_OR_UNB = 18956 Number of possible splits as detected by the pivoting preconditioner: 99195 Total time spent in the LP filter (creating and solving the LP): 139. Total time spent in subsit (constraint propagation): 10.7 Total time spent in reduced_interval_Newton (iteration to reduce the box): 585. Total time spent searching for "D" in the LP filter: 5.00 Total time spent actually solving the linear relaxations: 112. Total time spent doing linear algebra (preconditioners and solution processes): 417. LIST_BOOKKEEPING_TIME: 6.05 FUNCTION_EVALUATION_TIME (in forward_substitution): 80.2 Time spent setting up pivoting preconditioners: 29.0 Time spent computing pivoting preconditioners: 11.2 Time spent computing LP preconditioners: 27.9 Time spent computing inverse midpoint preconditioners: 13.9 Number of times MAXIT was exceeded in C_LP_DENSE: 845 Number of unbounded problems found in C_LP_DENSE: 9 Number Fritz-John matrix evaluations: 99339 Number of times SUBSIT decreased one or more coordinate widths: 19998 Number of times SUBSIT rejected a box: 4535 Total number of boxes processed in loop: 25011 N_FINDOPT_SUCCESS = 48 BEST_ESTIMATE: 0.212 Overall CPU time: 885. CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 585. =================================================== =================================================== 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: [ 0.556 , 0.558 ], [ 1.13 , 1.13 ] [ 0.621 , 0.623 ], [ 5.13 , 5.14 ] [ -4.94 , -4.93 ], [ 2.67 , 2.67 ] [ -2.07 , -2.07 ], [ 1.91 , 1.91 ] [ -1.10 , -1.10 ], [ 1.55 , 1.55 ] [ -0.582 , -0.580 ], [ 1.34 , 1.34 ] [ -0.229 , -0.227 ], [ 1.20 , 1.20 ] [ 0.410E-01, 0.430E-01 ], [ 0.605 , 0.607 ] [ 0.749 , 0.751 ] Rigorously verified bounds on the optimum, provided an optimum exists: [ 0.207 , 0.212 ]