Imagine I have a linear programming problem and somehow I am given an initial feasible non-basic solution. Is there a way to easily transform this solution into a basic feasible one that improves (in terms of the objective function value) over the value of the non-basic one?
In other words: is there a set of operations which can be applied to a non-basic feasible solution which produces a better or at least equal basic feasible solution? Ideally this set of operations would be constant ($O(1)$) or dependent on the number of variables of the problem ($O(n)$).