  Our contribution in this paper is two folded. We consider first the case of
linear programming with real coefficients and give a method which allows the
computation of a new upper bound on the distance from the origin to a feasible
point. Next we present an application of the ellipsoid method to form a novel
algorithm which allows one to search for the continuous convex functions
minimum without the prior knowledge on the search radius. If stopped early, the
proposed algorithm can give proofs that the optimal value has not been reached
yet, hence the user can opt for more iterations. However, if prior guarantees
exist on the existence of an optimum point in a given ball, the algorithm is
guaranteed to find it. For such a case we prove a polynomial upper bound on the
number of flops required to obtain the solution. The presented algorithm is
then applied to linear programming. We further develop our algorithm and
provide a method to answer the feasibility question of linear programs with
real coefficients in a number of flops bounded above by a polynomial in the
number of variables and the number of constraints. However, in case of
feasibility, our method does not generate an actual feasible point. For
obtaining such a point, we have to make some assumptions on the subgradients of
a certain function.

Optimization and Control