The routing capacity region of networks with multiple unicast sessions can be characterized using Farkas lemma as an infinite set of linear inequalities. In this paper this result is sharpened by exploiting properties of the solution satisfied by each rate-tuple on the boundary of the capacity...

In this paper, an interior-point based global filtering algorithm is proposed to solve linear programming problems with the right-hand-side and cost vectors being stochastic. Previous results on the limiting properties of the Kalman filtering process have been extended to handle some...

In this paper we derive a lower bound on the average complexity of the Simplex-Method as a solution-process for linear programs (LP) of the type: We assume these problems to be randomly generated according to the Rotation-Symmetry-Model: *Let a 1 ,…,a m , v be distributed independently,...

In this paper, we introduce a one-parametric class of smoothing functions which contains the Fischer–Burmeister smoothing function and the CHKS smoothing function as special cases. Based on this class of smoothing functions, a smoothing Newton algorithm is extended to solve linear programming...

In this paper, an extended form of the entropic perturbation method of linear programming is given, which can overcome the weakness of the original method – being easy of overflow in computing. Moreover, the global convergence of the gradient algorithm for the method is discussed. Copyright...

The dual simplex algorithm is the method of choice when linear programs have to be reoptimized after adding constraints or fixing variables. In this paper we discuss a modication of the standard dual simplex which allows for taking longer steps when proceeding from one dual feasible solution to...

Yamnitsky and Levin proposed a variant of Khachiyan's ellopsoid method for testing feasibility of systems of linear inequalities that also runs in polynomial time but uses simplices instead of ellipsoids. Starting with then-simplexS and the half-space {x¦a T x ≤ β}, the algorithm finds a...

This paper deals with the stability of the intersection of a given set $$ X\subset \mathbb{R}^{n}$$ with the solution, $$F\subset \mathbb{R}^{n}$$ , of a given linear system whose coefficients can be arbitrarily perturbed. In the optimization context, the fixed constraint set X can be the...

This paper analyzes numerically a long-term average stochastic control problem involving a controlled diffusion on a bounded region. The solution technique takes advantage of an infinite-dimensional linear programming formulation for the problem which relates the stationary measures to the...

We consider a discrete time Markov Decision Process (MDP) under the discounted payoff criterion in the presence of additional discounted cost constraints. We study the sensitivity of optimal Stationary Randomized (SR) policies in this setting with respect to the upper bound on the discounted...