By Baker Kearfott (early in 1995)

The code not only produces a putative global minimizer but also
verifies it using exhaustive branch and bound search

POWERSUM(8,18,44,114)  with bounds [-4,4]^4
 Box coordinates (the verified enclosure):
      0.9950D+00   0.1005D+01      0.1990D+01   0.2010D+01
      0.2985D+01   0.3015D+01      0.3980D+01   0.4000D+01
 Box contains the following approximate root:
   0.1000D+01   0.2000D+01   0.3000D+01   0.4000D+01

 Number of evaluations of a row of the point expanded Jacobi matrix: 206
 Number of bisections: 13467
 No. dense interval residual evaluations -- gradient code list: 73361
 Number of orig. system C-LP preconditioner rows: 133820
 Total number of forward_substitutions: 390011
 Number of Gauss--Seidel steps on the dense system: 133721
 Number of gradient evaluations from a gradient code list: 13471
 Total number of dense slope matrix evaluations: 134748
 Total number dense interval reduced gradient evaluations: 67374
 Total number of calls to ELFUNS for LANCELOT_OPT: 1
 Number of times a box was rejected in the interval Newton
 method due to an empty intersection: 748
 Number of times the interval Newton method made a coordinate
 interval smaller: 42184
 Number of times a box was rejected because of a large lower
 bound on the objective function: 12726
 Total time spent doing linear algebra (preconditioners
 and solution processes):  90.95 s
 Number of times the approximate solver was called: 1
 Number Fritz-John matrix evaluations: 33687
 Total number of boxes processed in loop: 26942
 Overall CPU time:   2.044E+03 s
 CPU time in PEEL_BOUNDARY:   2.000E-02 s
 CPU time in REDUCED_INTERVAL_NEWTON:   1.123E+03 s

These are the results of Kearfott's interval branch and bound 
algorithm that will soon be available. But the results are a year old 
and probably the final code will give different numbers.