The things we know, usually minimization of a convex function, unique solution will exist.My question is, maximization of a strictly convex function, will that give an unique maximum? If so how we can proof that. The objective function looks like below.max A e − ( d 0 + d 1 ) + B e − ( d 0 + d 1 + d 2 ) + CA,B and C are constants and d 0 , d 1 , d 2 are euclidean distances.

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The things we know, usually minimization of a convex function, unique solution will exist.My question is, maximization of a strictly convex function, will that give an unique maximum? If so how we can proof that. The objective function looks like below.max   A      e          −      (              d                  0                    +              d                  1                    )        +  B      e          −      (              d                  0                    +              d                  1                    +              d                  2                    )        +  CA,B and C are constants and       d          0        ,      d          1        ,      d          2       are euclidean distances.

Harold Cantrell · Accepted Answer

In general, the maximum of a strictly convex function over a convex set is not guaranteed to be bounded or unique. A sufficient counter example for boundedness is   f  (  x  )  =      x    2  , with a counterexample for uniqueness achieved by restricting   x to [−1,1].For this example (assuming       d    i    ≥  0), the maximum occurs at       d    0    =      d    1    =      d    2    =  0.

The things we know, usually minimization of a convex function, unique solution will exist. My q

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