A Validation Method to Integrate Non Linear Non Convex Constraints into Linear Programs

Abstract

Nowadays linear programming is the most robust method to solve optimization problems as it is the only one that if there is an optimal solution it will be found by this method, if not it will detect a problem with non feasible solutions. In practice many non linear programs are solved using linear approximations of the model. Non linearities can be present in the objective function and/or the constraints i.e. feasible region. The problem to deal with non linear constraints when this is convex has been already faced by converting the non linear constraint into a set of linear constraints. The problem which still has to be faced is when the non linear constraint is not convex too. In this situation, the optimal solution could lead to a solution outside the feasible region and therefore return a non feasible solution. This contribution deals with the detection of such possible solutions before the LP solver is applied. As to obteined results, they has been satisfactory for all the realized tests.