Output from FIND_GLOBAL_MIN on 05/05/2012 at 00:01:15. Version for the system is: March 13, 2009 Codelist file name is: ex5_2_2_case2_sourceG.CDL Box data file name is: ex5_2_2_case2_source.DT1 Initial box: [ -0.100E-03, 600. ], [ -0.100E-03, 200. ] [ -0.100E+05, 500. ], [ -0.100E+05, 500. ] [ -0.100E+05, 500. ], [ -0.100E+05, 500. ] [ -0.100E+05, 500. ], [ -0.100E+05, 500. ] [ -0.100E+05, 500. ] BOUND_CONSTRAINT: 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: 84351 Number of bisections: 157050 No. dense interval residual evaluations -- gradient code list: 3556787 Number of orig. system inverse midpoint preconditioner rows: 14088757 Number of orig. system C-LP preconditioner rows: 2507582 Number of solutions for a component in the expanded system: 39742981 Total number of forward_substitutions: 14919526 Number of Gauss--Seidel steps on the dense system: 20120998 Number point dense residual evaluations, gradient codelist: 3831967 Number of gradient evaluations from a gradient code list: 934506 Total number of dense slope matrix evaluations: 12259470 Total number second-order interval evaluations of the original function: 345189 Total number dense interval constraint evaluations: 176906892 Total number dense interval constraint gradient component evaluations: 1062655632 Total number dense point constraint gradient component evaluations: 624556980 Total number dense interval reduced gradient evaluations: 5322774 Total number of calls to FRITZ_JOHN_RESIDUALS: 1337578 Number of times a box was rejected because the constraints were not satisfied: 1413 Number of times a box was rejected because the gradient or reduced gradient did not contain zero: 13769 Average number of overall loop iterations in each call to the reduced interval Newton method): 6.83 Number of times a box was rejected in the interval Newton method due to an empty intersection: 16922 Number of times the interval Newton method made a coordinate interval smaller: 2608732 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 555131 Number of times a pivoting preconditioner was successful after the first sweep: 515039 Number of times a midpoint matrix was factored: 877818 Total number of times the reduced interval Newton method was tried: 197214 Number of times an inverse midpoint preconditioner led to improvement or rejection: 1008590 Number of times a C LP preconditioner led to improvement or rejection: 1061933 Number of times computing a C_LP failed 7517 N_C_LP_INFEASIBLE = 116424 N_LPF_INF_OR_UNB = 116424 Number of possible splits as detected by the pivoting preconditioner: 1323809 Total time spent in the LP filter (creating and solving the LP): 564. Total time spent in subsit (constraint propagation): 17.9 Total time spent in reduced_interval_Newton (iteration to reduce the box): 0.205E+04 Total time spent actually solving the linear relaxations: 521. Total time spent doing linear algebra (preconditioners and solution processes): 0.151E+04 Total time spent running the approximate optimizer: 17.9 LIST_BOOKKEEPING_TIME: 283. FUNCTION_EVALUATION_TIME (in forward_substitution): 84.7 Time spent setting up pivoting preconditioners: 129. Time spent computing pivoting preconditioners: 85.3 Time spent computing LP preconditioners: 276. Time spent computing inverse midpoint preconditioners: 56.0 Number of times MAXIT was exceeded in C_LP_DENSE: 32395 Number of unbounded problems found in C_LP_DENSE: 7517 Number of times the approximate solver was called: 31088 Number Fritz-John matrix evaluations: 1323809 Number of times SUBSIT decreased one or more coordinate widths: 129244 Number of times SUBSIT rejected a box: 28581 Number times a box was rejected due infeasible inequality constraints: 31724 Total number of boxes processed in loop: 225856 BEST_ESTIMATE: 0.210E+05 Overall CPU time: 0.720E+04 CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 0.205E+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: 84351 Interval hull of the unfathomed boxes: [ -0.100E-03, 600. ], [ -0.100E-03, 200. ] [ -0.223-307, 407. ], [ -0.223-307, 500. ] [ -0.223-307, 500. ], [ -0.223-307, 150. ] [ -0.223-307, 500. ], [ -0.223-307, 500. ] [ -0.223-307, 200. ] Rigorously verified bounds on the optimum, provided an optimum exists: [ -600. , 0.136E+05 ] FIRST UNFINISHED BOX: Box coordinates: [ 600. , 600. ], [ -0.140E-28, 0.727E-16 ] [ 300. , 300. ], [ 0.277E-01, 0.295E-01 ] [ 300. , 300. ], [ -0.223-307, 0.727E-16 ] [ 3.00 , 3.00 ], [ 300. , 300. ] [ -0.223-307, 0.901E-16 ] PHI: [ -600. , -600. ] Box does not contain an approximate root. Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.00 , 0.393E-17 ] Fritz John multipliers U: [ 0.00 , 0.786E-17 ], [ 0.275 , 0.281 ] [ 0.00 , 1.00 ], [ 0.00 , 0.339E-01 ] [ 0.00 , 0.142 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 0.717E-04 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 0.256 ] [ 0.00 , 0.142 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.274 , 0.424 ], [ 0.00 , 1.00 ] Fritz John multipliers V: [ -0.200E-16, 0.612E-16 ], [ -0.425E-16, 0.408E-16 ] [ 0.412 , 0.563 ], [ -0.196E-16, 0.668E-17 ] INEQ_CERT_FEASIBLE: F F T T F T T T T T T T F T T T T T F T NIN_POSS_BINDING: 5 LAST UNFINISHED BOX: Box coordinates: [ 413. , 424. ], [ -0.137E-12, 0.457 ] [ 131. , 143. ], [ 150. , 156. ] [ 119. , 125. ], [ -0.223-307, 0.367 ] [ 1.86 , 1.95 ], [ 288. , 299. ] [ -0.223-307, 0.957E-01 ] PHI: [ 558. , 897. ] Box does not contain an approximate root. Unknown = T Contains_root = F Fritz John multiplier U0: [ 0.00 , 0.104E-17 ] Fritz John multipliers U: [ 0.00 , 0.245E-04 ], [ 0.348 , 0.376 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 0.181 ], [ 0.00 , 1.00 ] [ 0.00 , 0.784 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 0.328E-02 ], [ 0.00 , 1.00 ] [ 0.00 , 0.191 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 1.00 ], [ 0.00 , 1.00 ] [ 0.00 , 0.168 ], [ 0.00 , 1.00 ] Fritz John multipliers V: [ -0.653E-23, 0.994E-20 ], [ -0.997E-17, 0.992E-17 ] [ 0.536 , 0.706 ], [ -0.136E-11, 0.441E-14 ] INEQ_CERT_FEASIBLE: T F T T F T T T T T T T F T T T T T F T NIN_POSS_BINDING: 4 Total volume of the boxes that have not yet been processed: 5.01799606214436536E+019