Infinite Linear Programs

We consider infinite linear programs, that is, linear programs with an infinite number of variables and constraints. The analysis of infinite linear programs is quite challenging due to the fact that many of the fundamental properties of finite-dimensional linear programming fall apart in infinite-dimensional spaces. We discuss the challenges in extending such fundamental concepts as basic feasible solutions and duality theory to infinite linear programs and the methods used to overcome these challenges. We survey the two main classes of infinite linear programs, countable infinite linear programs and continuous linear programs, and discuss the motivating applications of them. Keywords: countable infinite linear program; continuous linear program; finite-dimensional truncation; finite-dimensional discretization; continuous-time network flow problem

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