Conditions When the Problems of Linear Programming Are Algorithmically Unsolvable

Abstract

We study the properties of the constructive linear programming problems. The parameters of linear functions in such problems are constructive real numbers. Solving such a problem involves finding the optimal plan with the constructive real number components. We show that it is impossible to have an algorithm that solves an arbitrary constructive real programming problem.

Keywords

• constructive mathematics
• Halting problem
• decidable set
• enumerable set