Using Reduce inside Minimize

Ideas
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1 
Minimize[{x^2 - y^2, 
  Cos[x - y] >= 1/2, -5 <= x <= 5, -5 <= y <= 5}, {x, y}] (* returns unevaluated *)

Minimize[{x^2 - y^2, 
  Reduce[{Cos[x - y] >= 1/2, -5 <= x <= 5, -5 <= y <= 5}, {x, 
    y}]}, {x, y}] (* returns *)

 {1/9 (-150 \[Pi] + 25 \[Pi]^2), {x -> 5 - (5 \[Pi])/3, y -> 5}}
3 Likes
2

Useful technique.

Was there an implict question?

3

No specific question, I thought people might find this interesting or useful.

4

Neat observation, Frank, +1 :wink:

5

Frank, you may want to take a look at the following discussion:

** An Example of the symbolic Nature in Mathematica’s Numeric Process **

which was inspired by the very code you posted here.