Some Recent Developments in Infinite Programming

Infinite programming is concerned with optimization problems in which the number of variables and the number of constraints are both possibly infinite. If either the constraints or variables are finite in number then an infinite program is called a semi-infinite program. In this paper we review some recent work which has been carried out in infinite programming, in particular in the fields of semi-infinite linear programming, and continuous-time linear programming. Some discussion is made of theoretical issues such as the existence of solutions and duality theory, but we put a greater emphasis on endeavouring to summarize and explain some of the algorithmic developments in these areas.