I just started to use Wolfram Alpha Notebook Edition. I am using FindInstance command to evaluate the sign of an expression with $8$ variables, under simple constraints, but it takes too much time. Do you know if there is a mistake in this command syntax?

`FindInstance[a^2 (0.175 e+0.175 f+0.175 g+0.175 h)+a (e (0.3 b+0.1 \
c-0.1 d+0.3 f+0.25 g+0.125 h-0.35)+f (0.3 b+0.175 c-0.025 d+0.3 \
g+0.25 h-0.35)+0.3 b g+0.3 b h+0.25 c g+0.25 c h+0.05 d g+0.125 d \
h+0.175 e^2+0.175 f^2+0.175 g^2+0.3 g h-0.35 g+0.175 h^2-0.35 h)+b^2 \
(0.175 e+0.175 f+0.175 g+0.175 h)+b (e (0.225 c+0.025 d+0.3 f+0.175 \
g+0.05 h-0.35)+f (0.3 c+0.1 d+0.3 g+0.25 h-0.35)+0.3 c g+0.3 c \
h+0.175 d g+0.25 d h+0.175 e^2+0.175 f^2+0.175 g^2+0.3 g h-0.35 \
g+0.175 h^2-0.35 h)+0.175 c^2 e+0.175 c^2 f+0.175 c^2 g+0.175 c^2 \
h+0.15 c d e+0.225 c d f+0.3 c d g+0.3 c d h+0.175 c e^2+0.225 c e \
f+0.1 c e g-0.025 c e h-0.35 c e+0.175 c f^2+0.3 c f g+0.175 c f \
h-0.35 c f+0.175 c g^2+0.3 c g h-0.35 c g+0.175 c h^2-0.35 c h+0.1375 \
d^2 e+0.175 d^2 f+0.175 d^2 g+0.175 d^2 h+0.1375 d e^2+0.15 d e \
f+0.025 d e g-0.1 d e h-0.275 d e+0.175 d f^2+0.225 d f g+0.1 d f \
h-0.35 d f+0.175 d g^2+0.3 d g h-0.35 d g+0.175 d h^2-0.35 d h < 0 && \
a >= 2 && b >= 2 && c >= 2 && d >= 2 && e >= 2 && f >= 2 && g >= 2 && \
h >= 2, {a, b, c, d, e, f, g, h}]`
  • 3
    $\begingroup$ The numerically found minimum of the expression is 96.9 and it appears to be attained at {a -> 2., b -> 2., c -> 2., d -> 2., e -> 2., f -> 2., g -> 2., h -> 2.} so I don't think you'll get any solutions from FindInstance. All that remains is to prove that this is the true global minimum of the expression. $\endgroup$
    – flinty
    Commented Aug 15, 2020 at 15:43
  • 1
    $\begingroup$ Thank you @flinty, I was expecting a similar result. How did you obtain the minimum? Why does FindIstance take too much time? I was expecting then to obtain as a result of FindIstance "{}", i.e., there are no solutions. Usually it is faster than NMinimum and Minimum, right? $\endgroup$ Commented Aug 15, 2020 at 16:06
  • 3
    $\begingroup$ NMinimize[{expr, constraints}, vars] where expr is the objective without the < 0 at the end, constraints are all the >=2 constraints, and vars = {a,b,c,d,e,f,g,h}. No usually FindInstance is slower in large cases like this, and it has to prove there are no satisfying values to return {} an empty list - or it will give a warning that none could be found but it couldn't prove no solutions exist. $\endgroup$
    – flinty
    Commented Aug 15, 2020 at 16:15
  • 1
    $\begingroup$ Thank you once again @flinty $\endgroup$ Commented Aug 15, 2020 at 16:22
  • 1
    $\begingroup$ I would have another question @flinty: sometimes I get this error message "WolframAlpha::kbserr: Request to knowledgebase server api.wolframalpha.com failed with error code 400." Does it occur independently of the existence of any solution? $\endgroup$ Commented Aug 15, 2020 at 16:29


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