4
200*x1^3-200*x1*x2+x1-1;
-100*x1^2+ 1.10100000000000E+02*x2+ 9.90000000000000E+00*x4-20;
180*x3^3-180*x3*x4+x3-1;
-90*x3^2+ 9.90000000000000E+00*x2+ 1.00100000000000E+02*x4-20;
TITLE : system derived from optimizing the Wood function
ROOT COUNTS :
total degree : 36
3-homogeneous Bezout bound : 25
with partition : {x1 }{x2 x4 }{x3 }
mixed volume : 9
REFERENCES :
J.J. More, B.S. Garbow, K.E. Hillstrom:
`Testing unconstrained optimization software.'
Trans. Math. Software, Vol 7(1): 17-41, 1981.
( 10(x2-x1^2) )
( 1-x1 )
G(x)= ( 3sqrt(10)(x4-x3^2) )
( 1-x3 )
( sqrt(10)(x2+x4-2) )
((x2-x4)/sqrt(10) )
H(x):=DG^T(x).G(x)
THE SOLUTIONS :
9 4
===========================================================
solution 1 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.57355835612328E+00 2.84257851022096E-01
x2 : 2.39720627801032E+00 8.95148500287229E-01
x4 : -4.44855937693470E-01 -9.18847124013184E-01
x3 : -5.36397657592245E-01 8.60831364613137E-01
== err : 1.088E-13 = rco : 1.745E-04 = res : 9.484E-14 ==
solution 2 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -3.12510233943360E-02 2.14850736960187E-66
x2 : 1.65971386855783E-01 0.00000000000000E+00
x4 : 1.84263934696728E-01 -4.15431088876991E-66
x3 : -3.12581710232641E-02 4.74778387287990E-65
== err : 4.342E-16 = rco : 3.022E-01 = res : 2.442E-15 ==
solution 3 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -9.67974024937616E-01 1.03469743815115E-42
x2 : 9.47139140817886E-01 -2.00167411741164E-42
x4 : 9.51247665792282E-01 2.00247055853101E-42
x3 : -9.69516310331569E-01 -1.03464885797978E-42
== err : 1.716E-13 = rco : 1.054E-04 = res : 1.821E-14 ==
solution 4 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.57355835612330E+00 -2.84257851022089E-01
x2 : 2.39720627801038E+00 -8.95148500287217E-01
x4 : -4.44855937693522E-01 9.18847124013173E-01
x3 : -5.36397657592227E-01 -8.60831364613156E-01
== err : 5.759E-14 = rco : 1.745E-04 = res : 2.045E-13 ==
solution 5 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -5.36404369479206E-01 -8.60529486984931E-01
x2 : -4.45172990299157E-01 9.18999078613650E-01
x4 : 2.39751628227483E+00 -8.95297290755507E-01
x3 : 1.57359281312329E+00 -2.84279273572161E-01
== err : 9.315E-14 = rco : 2.029E-04 = res : 1.271E-13 ==
solution 6 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : 1.00000000000000E+00 -5.10349482937392E-57
x2 : 1.00000000000000E+00 -1.00501696737457E-56
x4 : 1.00000000000000E+00 1.00862631623573E-56
x3 : 1.00000000000000E+00 5.03441935978966E-57
== err : 2.934E-14 = rco : 5.987E-04 = res : 5.684E-14 ==
solution 7 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -1.03754146247809E+00 3.63159940802936E-01
x2 : 9.53900262105836E-01 -7.52084316235798E-01
x4 : 9.53161163420767E-01 7.52099393811562E-01
x3 : -1.03680791485365E+00 -3.63506283821887E-01
== err : 1.181E-13 = rco : 8.755E-05 = res : 6.355E-14 ==
solution 8 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -5.36404369479216E-01 8.60529486984926E-01
x2 : -4.45172990299139E-01 -9.18999078613661E-01
x4 : 2.39751628227481E+00 8.95297290755519E-01
x3 : 1.57359281312328E+00 2.84279273572166E-01
== err : 1.002E-13 = rco : 2.029E-04 = res : 1.608E-13 ==
solution 9 :
t : 1.00000000000000E+00 0.00000000000000E+00
m : 1
the solution for t :
x1 : -1.03754146247810E+00 -3.63159940802918E-01
x2 : 9.53900262105873E-01 7.52084316235769E-01
x4 : 9.53161163420728E-01 -7.52099393811532E-01
x3 : -1.03680791485363E+00 3.63506283821881E-01
== err : 1.549E-13 = rco : 8.755E-05 = res : 4.711E-14 ==