Output from FIND_GLOBAL_MIN on 05/07/2012 at 08:54:54. Version for the system is: March 13, 2009 Codelist file name is: ex6_2_6G.CDL Box data file name is: ex6_2_6.DT1 Initial box: [ 0.100E-05, 1.00 ], [ 0.100E-05, 1.00 ] [ 0.100E-05, 1.00 ] BOUND_CONSTRAINT: 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: [ 0.557E-01, 0.577E-01 ], [ 0.100E-05, 0.150E-02 ] [ 0.942 , 0.944 ] PHI: [ -0.195 , 0.194 ] Box contains the following approximate root: 0.567E-01, 0.751E-03, 0.943 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 0.454E-02, 0.454E-02 ] Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.665 , 0.665 ] Fritz John multipliers U: [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.335 , 0.335 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] Fritz John multipliers V: [ 0.376E-05, 0.376E-05 ] INEQ_CERT_FEASIBLE: T T F T T T NIN_POSS_BINDING: 1 ------------------------------------------------- LIST OF BOXES CONTAINING VERIFIED FEASIBLE POINTS: Box no.: 1 Box coordinates: [ 0.517 , 0.519 ], [ 0.501E-01, 0.521E-01 ] [ 0.430 , 0.432 ] PHI: [ -0.363 , 0.363 ] Box contains the following approximate root: 0.518 , 0.511E-01, 0.431 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 0.128E-04, 0.128E-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 ] Fritz John multipliers V: [ -1.00 , 1.00 ] INEQ_CERT_FEASIBLE: F F F F F F NIN_POSS_BINDING: 6 ------------------------------------------------- ALGORITHM COMPLETED WITH LESS THAN THE MAXIMUM NUMBER, 500000 OF BOXES. Number of bisections: 5279 No. dense interval residual evaluations -- gradient code list: 111860 Number of orig. system inverse midpoint preconditioner rows: 45810 Number of orig. system C-LP preconditioner rows: 34929 Number of solutions for a component in the expanded system: 1604281 Total number of forward_substitutions: 347831 Number of Gauss--Seidel steps on the dense system: 81356 Number point dense residual evaluations, gradient codelist: 17706 Number of gradient evaluations from a gradient code list: 34534 Total number of dense slope matrix evaluations: 104565 Total number second-order interval evaluations of the original function: 17346 Total number dense interval constraint evaluations: 1125098 Total number dense interval constraint gradient component evaluations: 1912767 Total number dense point constraint gradient component evaluations: 247401 Total number dense interval reduced gradient evaluations: 116438 Total number of calls to FRITZ_JOHN_RESIDUALS: 30547 Number of times a box was rejected because the constraints were not satisfied: 1 Number of times a box was rejected because the gradient or reduced gradient did not contain zero: 1473 Number of times feasible point was found based on the LP_FILTER approximate solution: 9 Average number of overall loop iterations in each call to the reduced interval Newton method): 3.47 Number of times a box was rejected in the interval Newton method due to an empty intersection: 1232 Number of times the interval Newton method made a coordinate interval smaller: 45646 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 28163 Number of times a pivoting preconditioner was successful after the first sweep: 15955 Number of times a midpoint matrix was factored: 8415 Total number of times the reduced interval Newton method was tried: 7986 Number of times an inverse midpoint preconditioner led to improvement or rejection: 6398 Number of times a C LP preconditioner led to improvement or rejection: 175 Number of times computing a C_LP failed 118 N_NEW_BEST_ESTIMATE_WITH_LP filter = 9 Number of possible splits as detected by the pivoting preconditioner: 26271 Total time spent in the LP filter (creating and solving the LP): 56.0 Total time spent in subsit (constraint propagation): 1.33 Total time spent in reduced_interval_Newton (iteration to reduce the box): 13.4 Total time spent searching for "D" in the LP filter: 0.616 Total time spent actually solving the linear relaxations: 47.7 Total time spent doing linear algebra (preconditioners and solution processes): 1.51 LIST_BOOKKEEPING_TIME: 1.24 FUNCTION_EVALUATION_TIME (in forward_substitution): 24.9 Time spent setting up pivoting preconditioners: 0.220 Time spent computing pivoting preconditioners: 0.308 Time spent computing LP preconditioners: 0.140 Time spent computing inverse midpoint preconditioners: 0.124 Number of times MAXIT was exceeded in C_LP_DENSE: 3 Number of unbounded problems found in C_LP_DENSE: 118 Number Fritz-John matrix evaluations: 29073 Number of times SUBSIT decreased one or more coordinate widths: 1440 Total number of boxes processed in loop: 7995 N_FINDOPT_SUCCESS = 933 BEST_ESTIMATE: 0.128E-04 Overall CPU time: 110. CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 13.4 =================================================== =================================================== 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: [ 0.517 , 0.519 ], [ 0.501E-01, 0.521E-01 ] [ 0.430 , 0.432 ] Interval hull of the small unverified boxes: [ 0.557E-01, 0.577E-01 ], [ 0.100E-05, 0.150E-02 ] [ 0.942 , 0.944 ] Rigorously verified bounds on the optimum, provided an optimum exists: [ -0.363 , 0.128E-04 ]