Equivalent Reformulations of Generalized Semi-infinite Min-Max Programming

Abstract

New equivalent reformulations of generalized semiinfinite 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.