Complete characterizations of global optimality for problems involving the pointwise minimum of sublinear functions

Necessary and sufficient global optimality conditions are presented for certain non-convex minimization problems subject to inequality constraints that are expressed as the pointwise minimum of sublinear (MSL) functions. A generalized Farkas lemma for inequality systems with MSL functions plays a crucial role in presenting the conditions in dual forms. Applications to certain multiplicative sublinear programming problems and fractional programming problems are also given