An Oblivious Ellipsoid Algorithm for Solving a System of (In)Feasible Linear Inequalities

The ellipsoid algorithm is a fundamental for computing solution to the system of m linear inequalities in n variables [Formula: see text] when its set solutions has positive volume. However, infeasible, no mechanism proving that (P) infeasible. This contrast other two algorithms tackling text], namely, simplex and interior-point methods, each which can be easily implemented way either produces or proves infeasible by producing alternative text]. paper develops an oblivious (OEA) Depending on dimensions condition measures, computational complexity basic OEA may worse than, same as, better than standard algorithm. We also present modified versions OEA, whose superior achieved first version infeasibility without second using more memory. Funding: J. Lamperski R. M. Freund were supported Air Force Office Scientific Research [Grant FA9550-19-1-0240].