Output from FIND_GLOBAL_MIN on 02/22/2001 at 10:26:11. Version for the system is: October 10, 2000 Codelist file name is: Neumaier_220_no_1G.CDL Box data file name is: Neumaier_220_no_1.DT1 Initial box: [ -0.1100D+02, 0.1100D+02 ] [ -0.1100D+02, 0.1100D+02 ] BOUND_CONSTRAINT: F F F F --------------------------------------- CONFIGURATION VALUES: EPS_DOMAIN: 0.1000D-08 MAXITR: 20000 MAX_CPU_SECONDS: 0.3600D+04 DO_INTERVAL_NEWTON: T QUADRATIC: T FULL_SPACE: F VERY_GOOD_INITIAL_GUESS: F USE_SUBSIT: T OUTPUT UNIT: 7 PRINT_LENGTH: 1 PHI_MUST_CONVERGE: T EQ_CNS_MUST_CONVERGE: T INEQ_CNS_MUST_CONVERGE: T PHI_THICKNESS_FACTOR: 0.5000D+00 EQ_CNS_THICKNESS_FACTOR: 0.5000D+00 INEQ_CNS_THICKNESS_FACTOR: 0.5000D+00 PHI_MUST_CONVERGE: T EQ_CNS_MUST_CONVERGE: T INEQ_CNS_MUST_CONVERGE: T PHI_CONVERGENCE_FACTOR: 0.1000D-13 EQ_CNS_CONVERGENCE_FACTOR: 0.1000D-13 INEQ_CNS_CONVERGENCE_FACTOR: 0.1000D-13 CONTINUITY_ACROSS_BRANCHES: F SINGULAR_EXPANSION_FACTOR: 0.1000D+02 HEURISTIC PARAMETER ALPHA: 0.5000D+00 APPROX_OPT_BEFORE_BISECTION: F 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: T Default point optimizer was used. THERE WERE NO BOXES IN THE LIST OF SMALL BOXES. LIST OF BOXES CONTAINING VERIFIED FEASIBLE POINTS: Box no.: 1 Box coordinates: [ -0.1016D+01, -0.1016D+01 ] [ 0.2566D+00, 0.2566D+00 ] PHI: [ 0.0000D+00, 0.6448D-18 ] B%LIUI(1,*): F F B%LIUI(2,*): F F B%SIDE(*): F F B%PEEL(*): T T Level: 4 Box contains the following approximate root: -0.1016D+01 0.2566D+00 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 0.0000D+00, 0.5292D-27 ] Unknown = T Contains_root = T Changed coordinates: T T U0: [ 0.0000D+00, 0.1000D+01 ] V: [ -0.1000D+01, 0.1000D+01 ] [ -0.1000D+01, 0.1000D+01 ] ------------------------------------------------- Box no.: 2 Box coordinates: [ -0.2566D+00, -0.2566D+00 ] [ 0.1016D+01, 0.1016D+01 ] PHI: [ 0.0000D+00, 0.2521D-17 ] B%LIUI(1,*): F F B%LIUI(2,*): F F B%SIDE(*): F F B%PEEL(*): T T Level: 4 Box contains the following approximate root: -0.2566D+00 0.1016D+01 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 0.0000D+00, 0.4793D-27 ] Unknown = T Contains_root = T Changed coordinates: T T U0: [ 0.0000D+00, 0.1000D+01 ] V: [ -0.1000D+01, 0.1000D+01 ] [ -0.1000D+01, 0.1000D+01 ] ------------------------------------------------- Box no.: 3 Box coordinates: [ 0.2566D+00, 0.2566D+00 ] [ -0.1016D+01, -0.1016D+01 ] PHI: [ 0.0000D+00, 0.2521D-17 ] B%LIUI(1,*): F F B%LIUI(2,*): F F B%SIDE(*): F F B%PEEL(*): T T Level: 4 Box contains the following approximate root: 0.2566D+00 -0.1016D+01 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 0.0000D+00, 0.5416D-27 ] Unknown = T Contains_root = T Changed coordinates: T T U0: [ 0.0000D+00, 0.1000D+01 ] V: [ -0.1000D+01, 0.1000D+01 ] [ -0.1000D+01, 0.1000D+01 ] ------------------------------------------------- Box no.: 4 Box coordinates: [ 0.1016D+01, 0.1016D+01 ] [ -0.2566D+00, -0.2566D+00 ] PHI: [ 0.0000D+00, 0.6447D-18 ] B%LIUI(1,*): F F B%LIUI(2,*): F F B%SIDE(*): F F B%PEEL(*): T T Level: 4 Box contains the following approximate root: 0.1016D+01 -0.2566D+00 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 0.0000D+00, 0.4200D-27 ] Unknown = T Contains_root = T Changed coordinates: T T U0: [ 0.0000D+00, 0.1000D+01 ] V: [ -0.1000D+01, 0.1000D+01 ] [ -0.1000D+01, 0.1000D+01 ] ------------------------------------------------- Box no.: 5 Box coordinates: [ -0.7412D+00, -0.7412D+00 ] [ 0.7412D+00, 0.7412D+00 ] PHI: [ 0.0000D+00, 0.6053D-18 ] B%LIUI(1,*): F F B%LIUI(2,*): F F B%SIDE(*): F F B%PEEL(*): T T Level: 5 Box contains the following approximate root: -0.7412D+00 0.7412D+00 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 0.2416D-29, 0.3590D-27 ] Unknown = T Contains_root = T Changed coordinates: T T U0: [ 0.0000D+00, 0.1000D+01 ] V: [ -0.1000D+01, 0.1000D+01 ] [ -0.1000D+01, 0.1000D+01 ] ------------------------------------------------- Box no.: 6 Box coordinates: [ 0.7412D+00, 0.7412D+00 ] [ -0.7412D+00, -0.7412D+00 ] PHI: [ 0.0000D+00, 0.6053D-18 ] B%LIUI(1,*): F F B%LIUI(2,*): F F B%SIDE(*): F F B%PEEL(*): T T Level: 5 Box contains the following approximate root: 0.7412D+00 -0.7412D+00 OBJECTIVE ENCLOSURE AT APPROXIMATE ROOT: [ 0.2416D-29, 0.3590D-27 ] Unknown = T Contains_root = T Changed coordinates: T T U0: [ 0.0000D+00, 0.1000D+01 ] V: [ -0.1000D+01, 0.1000D+01 ] [ -0.1000D+01, 0.1000D+01 ] ------------------------------------------------- ALGORITHM COMPLETED WITH LESS THAN THE MAXIMUM NUMBER, 20000 OF BOXES. Number of bisections: 13 No. dense interval residual evaluations -- gradient code list: 236 Number of orig. system inverse midpoint preconditioner rows: 12 Number of orig. system C-LP preconditioner rows: 62 Number of solutions for a component in the expanded system: 15784 Total number of forward_substitutions: 790 Number of Gauss--Seidel steps on the dense system: 56 Number of gradient evaluations from a gradient code list: 40 Total number of dense slope matrix evaluations: 90 Total number second-order interval evaluations of the original function: 90 Total number dense interval constraint evaluations: 452 Total number dense interval constraint gradient component evaluations: 364 Total number dense point constraint gradient component evaluations: 28 Number of times the interval Newton method made a coordinate interval smaller: 34 Total time spent doing linear algebra (preconditioners and solution processes): 5.000000000000004E-002 Number of times the approximate solver was called: 7 Number of times SUBSIT decreased one or more coordinate widths: 13 Number of times SUBSIT rejected a box: 8 Total number of boxes processed in loop: 27 BEST_ESTIMATE: 0.0000D+00 Overall CPU time: 0.5500D+00 CPU time in PEEL_BOUNDARY: 0.0000D+00 CPU time in REDUCED_INTERVAL_NEWTON: 0.6000D-01