In this paper we present necessary conditions for global optimality for polynomial problems with box or bivalent constraints using separable polynomial relaxations. We achieve this by first deriving a numerically checkable characterization of global optimality for separable polynomial problems...

We develop a duality theory for minimax fractional programming problems in the face of data uncertainty both in the objective and constraints. Following the framework of robust optimization, we establish strong duality between the robust counterpart of an uncertain minimax convex–concave...

We present geometric criteria for a feasible point that satisfies the Kuhn-Tucker conditions to be a global minimizer of mathematical programming problems with or without bounds on the variables. The criteria apply to multi-extremal programming problems which may have several local minimizers...