Many practical problems with important values can be modeled as distributionally robust optimization problems, which often exist distributional ambiguity. This paper aims at studying minimax distributionally robust optimization problem based on -divergence function. First of all, ambiguous set of distribution Pis constructed with -divergence function. Second, applying the change-of-measure technique, the inner maximization problem with respect to distribution Pis converted to a convex optimization problem with respect to likelihood ratio (LR). Moreover, existence of solution of the inner maximization problem is proved using the duality theory. Finally, an equivalent form of the inner maximization problem is established.

-divergence function, likelihood ratio, distributionally robust optimization, change-of-measure technique.