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Wolfram|Alpha Optimization

Identifying constants in maximization problem in Wolfram|Alpha

Tyler Hoyer

Posted 10 years ago

I'm trying to maximize x in the following equation: xa - 2xyb + 2xc + y^2d - 2ye - f^2 + 2r^2 where x and y are variables both between -1 and 1, and the rest are given constants. Wolfram Alpha says there is no global maximum when I input "maximize x where xa - 2xyb + 2xc + y^2d - 2ye = f^2 - 2r^2 and x <= 1 and x >= -1 and y <= 1 and y >= -1." From my previous calculations and the problem I'm solving, I know that there is a maximum. I think that Wolfram Alpha is interpreting constants a through f as variables instead of constants. How can I tell Wolfram Alpha to solve it interpreting a through f as constants?

POSTED BY: Tyler Hoyer

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S M Blinder

S M Blinder, WRI and Univ of Michigan

Posted 10 years ago

Seeking a maximum with respect to all the variables, you would find In[11]:= FindMaximum[ x a - 2 x y b + 2 x c + y^2 d - 2 y e - f^2 + 2 r^2, {x, y, a, b, c, d, e, f, r}] During evaluation of In[11]:= FindMaximum::cvmit: Failed to converge to the requested accuracy or precision within 100 iterations. >> Out[11]= {2.37845911570793310^309, {x -> 1.2316410^102, y -> -1.7979910^103, a -> 6.3046810^102, b -> -1.485510^103, c -> 1.2609410^103, d -> 9.392510^102, e -> -1.3949410^103, f -> -1.3949410^103, r -> 2.2769510^103}}

Seeking a maximum with respect to all the variables, you would find

In[11]:= FindMaximum[
 x a - 2 x y b + 2 x c + y^2  d - 2 y e - f^2 + 2 r^2, {x, y, a, b, c,
   d, e, f, r}]

During evaluation of In[11]:= FindMaximum::cvmit: Failed to converge to the requested accuracy or precision within 100 iterations. >>

Out[11]= {2.378459115707933*10^309, {x -> 1.23164*10^102, 
  y -> -1.79799*10^103, a -> 6.30468*10^102, b -> -1.4855*10^103, 
  c -> 1.26094*10^103, d -> 9.3925*10^102, e -> -1.39494*10^103, 
  f -> -1.39494*10^103, r -> 2.27695*10^103}}

POSTED BY: S M Blinder

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