| We present an interval algorithm for solving discrete minimax problems where the constituent minimax functions are continuously differentiable functions of one real variable. Our approach is based on smoothing the max-type function by exploiting the Jaynes's maximum entropy [Phys. Rev., 106:620-630, 1957]. The algorithm works within the branch-and-bound framework and uses first order information of the entropic objective function by means of an interval evaluation. First order information aids threefold. Firstly, to check monotonicity. Secondly, to apply mean value form for bounding the range of the function, and finally, to prune the search interval using the current upper bound of the global minimum. Our numerical results show that the proposed algorithm guarantees computationally rigorous bounds for the global minimum and all global minimizers. |
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