Classifying convex extremum problems over linear topologies having separation properties

Mathematics Technical Repor

On Balanced Sets, Cores, and Linear Programming

On Balanced Sets, Cores, and Linear Programmin

Fenchel-duality and separably-infinite programs

In two recent papers Chabnes, Gbibie, and Kortanek studied a special class of infinite linear programs where only a finite number of variables appear in an infinite number of constraints and where only a finite number of constraints have an infinite number of variables. Termed separably-infinite programs, their duality was used to characterize a class of saddle value problems as a uniextremai principle. We show how this characterization can be derived and extended within Fenchel and Rockafellar duality, and that the values of the dual separably-infinite programs embrace the values of the Fenchel dual pair within their interval. The development demonstrates that the general finite dimensional Fenchel dual pair is equivalent to a dual pair of separably-infinite programs when certain cones of coefficients are closed

Analytical properties of some multiple-source urban diffusion models

It is generally required that the concentration of a certain pollutant at any given point ( x, y ) shall be below a maximum amount defined by a known function S (x, y ). In this paper we analyze different ways of relating the emission rates of polluters with the resultant concentration Q (x, y ) by means of various transfer functions. We discuss the analytical properties of the transfer functions which can be derived from various well-known diffusion models. We also discuss a simple instance of optimization models of a type, introduced by Gorr and Kortanek (1970).