Output from FIND_GLOBAL_MIN on 05/04/2012 at 17:43:58. Version for the system is: March 13, 2009 Codelist file name is: ex4_1_9G.CDL Box data file name is: ex4_1_9.DT1 Initial box: [ 0.00 , 3.00 ], [ 0.00 , 4.00 ] BOUND_CONSTRAINT: 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: [ 2.33 , 2.33 ], [ 3.18 , 3.18 ] PHI: [ -5.51 , -5.50 ] Box contains the following approximate root: 2.33 , 3.18 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ -5.51 , -5.51 ] 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 ] 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: 178 No. dense interval residual evaluations -- gradient code list: 3763 Number of orig. system inverse midpoint preconditioner rows: 2298 Number of orig. system C-LP preconditioner rows: 804 Number of solutions for a component in the expanded system: 115098 Total number of forward_substitutions: 9649 Number of Gauss--Seidel steps on the dense system: 3193 Number point dense residual evaluations, gradient codelist: 88 Number of gradient evaluations from a gradient code list: 1229 Total number of dense slope matrix evaluations: 2084 Total number second-order interval evaluations of the original function: 508 Total number dense interval constraint evaluations: 36390 Total number dense interval constraint gradient component evaluations: 43188 Total number dense point constraint gradient component evaluations: 1188 Total number dense interval reduced gradient evaluations: 3131 Total number of calls to FRITZ_JOHN_RESIDUALS: 794 Number of times a box was rejected because the gradient or reduced gradient did not contain zero: 6 Number of times feasible point was found based on the LP_FILTER approximate solution: 1 Average number of overall loop iterations in each call to the reduced interval Newton method): 2.95 Number of times a box was rejected in the interval Newton method due to an empty intersection: 73 Number of times the interval Newton method made a coordinate interval smaller: 851 Number of times a pivoting preconditioner made a coordinate interval smaller or rejected a coordinate: 353 Number of times a pivoting preconditioner was successful after the first sweep: 205 Number of times a midpoint matrix was factored: 433 Total number of times the reduced interval Newton method was tried: 258 Number of times an inverse midpoint preconditioner led to improvement or rejection: 302 Number of times a C LP preconditioner led to improvement or rejection: 135 N_C_LP_INFEASIBLE = 234 N_NEW_BEST_ESTIMATE_WITH_LP filter = 1 N_LPF_INF_OR_UNB = 234 Number of times a C LP preconditioner was not computed because the heuristic determined it was not worth it: 139 Number of possible splits as detected by the pivoting preconditioner: 755 Total time spent in the LP filter (creating and solving the LP): 0.548 Total time spent in subsit (constraint propagation): 0.104 Total time spent in reduced_interval_Newton (iteration to reduce the box): 0.108 Total time spent searching for "D" in the LP filter: 0.800E-02 Total time spent actually solving the linear relaxations: 0.484 Total time spent doing linear algebra (preconditioners and solution processes): 0.280E-01 LIST_BOOKKEEPING_TIME: 0.400E-02 FUNCTION_EVALUATION_TIME (in forward_substitution): 0.240E-01 Time spent setting up pivoting preconditioners: 0.400E-02 Time spent computing LP preconditioners: 0.400E-02 Time spent computing inverse midpoint preconditioners: 0.800E-02 Number Fritz-John matrix evaluations: 788 Number of times SUBSIT decreased one or more coordinate widths: 35 Number of times SUBSIT rejected a box: 97 Number times a box was rejected due infeasible inequality constraints: 1 Total number of boxes processed in loop: 356 N_FINDOPT_SUCCESS = 11 BEST_ESTIMATE: -5.51 Overall CPU time: 0.896 CPU time in PEEL_BOUNDARY: 0.00 CPU time in REDUCED_INTERVAL_NEWTON: 0.108 =================================================== =================================================== 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: [ 2.33 , 2.33 ], [ 3.18 , 3.18 ] Rigorously verified bounds on the optimum, provided an optimum exists: [ -5.51 , -5.51 ]