Linear Programming - A brute force approach

Question

I was wondering what the main drawback for using a brute force approach in Linear Programming would be. My idea would be to just iterate over all possible basic solutions, filter out the infeasible ones and pick the one that minimises the given linear function. How would this fare compared to more sophisticated methods?

Answer 1

Of course everything depends upon the problem at hand. For small problems brute force may be appropriate but it is very easy indeed to create realistic problems for which brute force would exhaust all the computing and memory resources of the universe.

The performance of a brute force search stopped pre-maturely depends entirely on the starting conditions and the nature and scale of the problem.