Timeline for When does symmetry in an optimization problem imply that all variables are equal at optimality?
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| Mar 18, 2011 at 14:18 | comment | added | Igor Rivin | @Robert indeed, that is the precise statement... | |
| Mar 18, 2011 at 0:01 | comment | added | Robert Israel | Or more precisely, at least one minimizer is invariant. If the objective function is strictly convex, the minimizer is unique, and then it must be invariant, but otherwise there could also be non-invariant minimizers. For example, in two dimensions take f(x,y) = max(x^2 + y^2 - 1, 0) which is convex and invariant under rotations; the minimizers constitute the closed unit disk, and only (0,0) is invariant. | |
| Mar 17, 2011 at 14:20 | history | answered | Igor Rivin | CC BY-SA 2.5 |