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On a strictly convex and strictly sub-additive cost function with positive fixed cost

Tanaka, Yasuhito and Hattori, Masahiko (2017): On a strictly convex and strictly sub-additive cost function with positive fixed cost.

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Abstract

We investigate the existence of a strictly convex and strictly sub-additive cost function with positive fixed cost. If there is a positive fixed cost, any cost function can not be super-additive, and concavity (including linearity) of cost function implies strict sub-additivity. Then, does there exist a strictly convex and strictly sub-additive cost function? We will present such a cost function. It is close to a linear function although it is strictly convex.

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