Output from FIND_GLOBAL_MIN on 05/02/2012 at 12:35:30. Version for the system is: March 13, 2009 Codelist file name is: ex9_1_9G.CDL Box data file name is: ex9_1_9.DT1 Initial box: [ 0.00 , 0.100E+05 ], [ 0.00 , 0.100E+05 ] [ 0.00 , 0.100E+05 ], [ 0.00 , 0.100E+05 ] [ 0.00 , 0.100E+05 ], [ 0.00 , 0.100E+05 ] [ 0.00 , 0.100E+05 ], [ 0.00 , 0.100E+05 ] [ 0.00 , 0.100E+05 ], [ 0.00 , 0.100E+05 ] [ 0.00 , 0.100E+05 ], [ 0.00 , 0.100E+05 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 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. THERE WERE NO BOXES CORRESPONDING TO VERIFIED FEASIBLE POINTS. ALGORITHM COULD NOT COMPLETE IN 0.7200D+04 SECONDS OF CPU TIME. Number of boxes that have not yet been processed: 182724 Number of bisections: 186668 No. dense interval residual evaluations -- gradient code list: 2842535 Number of orig. system inverse midpoint preconditioner rows: 5641877 Number of orig. system C-LP preconditioner rows: 4447120 Number of solutions for a component in the expanded system: 17380981 Total number of forward_substitutions: 18400085 Number of Gauss--Seidel steps on the dense system: 13156550 Number point dense residual evaluations, gradient codelist: 22 Number of gradient evaluations from a gradient code list: 945163 Total number of dense slope matrix evaluations: 10189663 Total number second-order interval evaluations of the original function: 373336 Total number dense interval constraint evaluations: 169439766 Total number dense interval constraint gradient component evaluations: 1730566816 Total number dense point constraint gradient component evaluations: 142120 Total number dense interval reduced gradient evaluations: 2312604 Total number of calls to FRITZ_JOHN_RESIDUALS: 578871 Number of times a box was rejected because the constraints were not satisfied: 2 Number of times a box was rejected because the gradient or reduced gradient did not contain zero: 1440 Average number of overall loop iterations in each call to the reduced interval Newton method): 3.04 Number of times a box was rejected in the interval Newton method due to an empty intersection: 2499 Number of times the interval Newton method made a coordinate interval smaller: 1221667 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 143612 Number of times a pivoting preconditioner was successful after the first sweep: 91877 Number of times a midpoint matrix was factored: 478035 Total number of times the reduced interval Newton method was tried: 190609 Number of times an inverse midpoint preconditioner led to improvement or rejection: 783504 Number of times a C LP preconditioner led to improvement or rejection: 297050 Number of times computing a C_LP failed 34 Number of times a C LP preconditioner was not computed because the heuristic determined it was not worth it: 4 Number of possible splits as detected by the pivoting preconditioner: 577431 Total time spent in the LP filter (creating and solving the LP): 532. Total time spent in subsit (constraint propagation): 10.8 Total time spent in reduced_interval_Newton (iteration to reduce the box): 0.497E+04 Total time spent actually solving the linear relaxations: 466. Total time spent doing linear algebra (preconditioners and solution processes): 0.331E+04 Total time spent running the approximate optimizer: 0.280E-01 LIST_BOOKKEEPING_TIME: 0.148E+04 FUNCTION_EVALUATION_TIME (in forward_substitution): 126. Time spent setting up pivoting preconditioners: 211. Time spent computing pivoting preconditioners: 62.2 Time spent computing LP preconditioners: 583. Time spent computing inverse midpoint preconditioners: 58.3 Number of times MAXIT was exceeded in C_LP_DENSE: 124 Number of unbounded problems found in C_LP_DENSE: 34 Number of times the approximate solver was called: 1 Number Fritz-John matrix evaluations: 577431 Number of times SUBSIT decreased one or more coordinate widths: 114493 Number times a box was rejected due infeasible inequality constraints: 1 Total number of boxes processed in loop: 190609 BEST_ESTIMATE: 0.200E+05 Overall CPU time: 0.720E+04 CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 0.497E+04 =================================================== =================================================== Number of boxes in the list with proven feasible points: 0 Number of boxes in the list of other small boxes: 0 Number of unfathomed boxes: 182724 Interval hull of the unfathomed boxes: [ 0.880 , 6.80 ], [ 0.00 , 3.56 ] [ 0.00 , 6.00 ], [ 0.00 , 2.50 ] [ 0.00 , 6.00 ], [ 0.00 , 5.60 ] [ 0.00 , 3.56 ], [ 0.00 , 10.0 ] [ 0.00 , 10.0 ], [ 0.00 , 10.0 ] [ 0.00 , 7.00 ], [ 0.00 , 10.0 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ] Rigorously verified bounds on the optimum, provided an optimum exists: [ 1.83 , 10.4 ] FIRST UNFINISHED BOX: Box coordinates: [ 1.83 , 2.00 ], [ 0.00 , 0.165 ] [ 0.00 , 0.258E-05 ], [ 2.13 , 2.50 ] [ 6.00 , 6.00 ], [ 0.00 , 0.826 ] [ 0.00 , 0.330 ], [ 2.50 , 4.13 ] [ 2.94 , 3.75 ], [ 0.00 , 0.823 ] [ 0.00 , 0.406 ], [ 1.10 , 1.91 ] [ 0.500 , 0.750 ], [ 0.294 , 0.500 ] [ 0.165 , 0.329 ], [ 0.00 , 0.125 ] [ 0.500 , 0.750 ] PHI: [ 1.83 , 2.17 ] Box does not contain an approximate root. Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.268 , 0.423 ] Fritz John multipliers U: [ 0.00 , 0.958E-16 ], [ 0.00 , 0.387E-28 ] [ 0.00 , 0.133E-28 ], [ 0.00 , 0.558E-16 ] [ 0.00 , 1.00 ], [ 0.00 , 0.220E-15 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 0.946E-16 ] [ 0.00 , 1.00 ], [ 0.00 , 0.215 ] [ 0.248 , 0.545 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 0.154 ] [ 0.00 , 0.479 ], [ 0.00 , 0.864E-16 ] [ 0.00 , 0.383E-01 ], [ 0.00 , 0.348E-16 ] [ 0.00 , 0.798E-16 ], [ 0.00 , 0.429E-29 ] [ 0.00 , 1.00 ], [ 0.00 , 0.398E-14 ] [ 0.00 , 0.412E-27 ], [ 0.00 , 1.00 ] [ 0.00 , 0.899E-16 ], [ 0.00 , 1.00 ] [ 0.00 , 0.912E-16 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 0.568E-16 ] Fritz John multipliers V: [ 0.248 , 0.545 ], [ -0.135E-28, 0.135E-28 ] [ -0.117E-28, 0.117E-28 ], [ -0.847E-15, 0.154 ] [ -0.233E-14, 0.479 ], [ -0.271E-29, 0.271E-29 ] INEQ_CERT_FEASIBLE: T F T F T T T T T T T F F T T F F T T F F T T T T T T T F T T T NIN_POSS_BINDING: 9 LAST UNFINISHED BOX: Box coordinates: [ 3.84 , 6.80 ], [ 0.00 , 3.56 ] [ 0.00 , 6.00 ], [ 0.00 , 2.50 ] [ 0.00 , 6.00 ], [ 0.00 , 5.60 ] [ 0.00 , 3.56 ], [ 0.00 , 10.0 ] [ 5.00 , 10.0 ], [ 0.00 , 10.0 ] [ 3.50 , 7.00 ], [ 0.00 , 5.00 ] [ 0.00 , 1.00 ], [ 0.500 , 1.00 ] [ 0.00 , 1.00 ], [ 0.350 , 1.00 ] [ 0.00 , 1.00 ] PHI: [ 3.84 , 10.4 ] Box does not contain an approximate root. Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.00 , 1.00 ] Fritz John multipliers U: [ 0.00 , 1.00 ], [ 0.00 , 0.994E-14 ] [ 0.00 , 1.00 ], [ 0.00 , 0.198E-13 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 0.169E-12 ], [ 0.00 , 1.00 ] [ 0.00 , 0.236 ], [ 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 , 0.114E-12 ] [ 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 ], [ -0.193E-12, 1.00 ] [ -1.00 , 1.00 ], [ -0.236 , 1.00 ] [ -1.00 , 1.00 ], [ -0.350E-14, 0.113E-12 ] INEQ_CERT_FEASIBLE: F F F F F F F F F F T F F F F F F F T F T F F F T F F F T F F F NIN_POSS_BINDING: 27 Total volume of the boxes that have not yet been processed: 426646041.29470235