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3 months ago
I know that Slater's condition implies strong duality and that the dual problem's supremum is attained. Is the infimum for the primal also attained under Slater's condition?
Nov 28, 2022 at 1:20
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It has no reason to be. For example, if you minimize
$y$ subject to $y \ge e^x$ (that is, $e^x-y \le 0$) then the infimum is not attained; however, a point like $(0,2)$ shows that Slater's condition is satisfied.
Nov 28, 2022 at 1:33
Misha Lavrov Misha Lavrov
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