New equivalent reformulations of generalized semi-infinite min-max programming (GSMMP) is derived by addressing the perturbed problem of the lower-level programming. Based on these, we obtain an exact penalty representations for the lower-level programming, which allows us to convert (GSSMP) into the standard semi-infinite programming problems (SMMP) via a class of exact penalty functions, including not only the function used in [9] but also some smooth exact penalty functions as special cases. This fact makes it possible to solve (GSMMP) by using any available standard semi-infinite optimization algorithms.
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