The multicommodityow probleminvolves simultaneouslyship-ping multiplecommoditiesthrough a single network so that the total amount of ow on each edge is no more than the capacity of the edge. This problem can be expressed as a large linear program, and most known algorithms for it, both theoretical and practical, are linear programming algorithms designed to take advantage of the structure of mu...

We describe a primal-dual interior point algorithm for a class of convex separable programming problems subject to linear constraints. Each iteration updates a penalty parameter and finds a Newton step associated with the Karush-Kuhn-Tucker system of equations which characterizes a solution of the logarithmic barrier function problem for that parameter. It is shown that the duality gap is reduc...

In this paper, we evaluate traversable wormhole solutions through Karmarkar condition in f(R, T) theory, where T is the trace of energy-momentum tensor and R represents Ricci scalar. We develop a shape function for static geometry by using embedding class-I technique. The resulting used to construct that fulfills all necessary conditions joins two asymptotically flat regions spacetime. investig...

This paper provides another derivation of the Karmarkar direction for linear programming. It is strongly motivated by derivations of Gonzaga, but we show how the direction can be viewed as a steepest descent direction in the original feasible region corresponding to a metric diierent from the Euclidean one. We show that a xed decrease in the potential function can be obtained by taking a step i...

the concept of comprehensive grobner bases was introduced by weispfenning. montes has proposed an efficient algorithm for computing these bases. but he has not explicitly used buchberger's criteria in his algorithm. in this paper we prove that we can apply these criteria on montes algorithm. we propose a modified version of montes algorithm and evaluate its performance via some examples.