In this paper, we will study optimality conditions of semi-infinite programs and generalized semi-infinite programs, for which the gradient objective function when evaluated at any feasible direction for the linearized constraint set is non-negative. We consider three types of penalty functions for semi-infinite program and investigate the relationship among the exactness of these penalty funct...

For an upper semi-continuous set-valued mapping from one topological space to another and for a lower semi-continuous function defined on the product of these spaces, Berge’s theorem states lower semi-continuity of the minimum of this function taken over the image sets. It assumes that the image sets are compact. For Hausdorff topological spaces, this paper extends Berge’s theorem to set-valued...

This note provides a price equilibrium existence theorem in economies where commodities may be indivisible and aggregate excess demand functions may be discontinuous or do not have any structure except Walras’ Law. We establish a condition, called recursive transfer lower semi-continuity, which is weaker than transfer lower semi-continuity and in turn weaker than lower semi-continuity, for the ...

Abstract. Both the scientific and operational communities are increasingly interested in subseasonal to seasonal variations of weather climate. The semi-annual oscillation (SAO) has been studied extensively at surface as well middle atmosphere (upper stratosphere lower mesosphere). However, SAO upper troposphere (UTLS) less discussed. Here we find evident temperature UTLS (250–175 hPa) from sub...