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Answered by redracoon
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The conjugate function f* (y) is the maximum gap between the linear function yx and the function f (x). Example 1 (Affine function) f (x) = ax + b. By definition, the conjugate function is given by f∗ (y) = supx (yx − ax − b). As a function of x, the difference is bounded iff y−a = 0.

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