We propose a polynomial time primal-dual potential reduction algorithm for linear programming. Unlike any other interior point method, the new algorithm is based on a rank-one updating scheme for sequentially computing the projection matrices. For a standard linear programming problem, the...

AMS classifications: 90C22; 90C20;

In this paper we study several issues related to the characterization of speci c classes of multivariate quadratic mappings that are nonnegative over a given domain, with nonnegativity de ned by a pre-speci ed conic order.In particular, we consider the set (cone) of nonnegative quadratic...

We propose a polynomial time primal-dual potential reduction algorithm for linear programming. Unlike any other interior point method, the new algorithm is based on a rank-one updating scheme for sequentially computing the projection matrices. For a standard linear programming problem, the...

In this paper we will describe a Multi-Agent System which is capable of finding a feasible solution of a specially structured linear programming problem. Emphasis is given to correctness issues and termination detection.

In this paper we generalize the so-called first-in-last-out pivot rule and the most-often-selected-variable pivot rule for the simplex method, as proposed in Zhang \cite{Z91}, to the criss-cross pivot setting where neither the primal nor the dual feasibility is preserved. The finiteness of the...