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...

We study the problem of optimally controlling a multiserver queueing system. Customers arrive in a Poisson fashion and join a single queue, served by N servers, S 1 ,S 2 ,… , S N . The servers have different rates. The service times at each server are independent and exponentially distributed....

In this paper, we propose a second order interior point algorithm for symmetric cone programming using a wide neighborhood of the central path. The convergence is shown for commutative class of search directions. The complexity bound is $${O(r^{3/2}\,\log\epsilon^{-1})}$$ for the NT methods, and...

We propose an optimal schedule for multiple classes of arrivals in a queueing system consisting of queues in tandem. The arrival process for each class is Poisson with different rates, and the service times are constant. A theoretical result is presented by Linear Programming of sample-path...

This paper uses linear programming to numerically evaluate the Laplace transform of the exit time distribution and the resolvent of the moments of various Markov processes in bounded regions. The linear programming formulation is developed from a martingale characterization of the processes and...

We consider zero-sum Markov games with incomplete information. Here, the second player is never informed about the current state of the underlying Markov chain. The existence of a value and of optimal strategies for both players is shown. In particular, we present finite algorithms for computing...

We consider discrete time Markov Decision Process (MDP) with finite state and action spaces under average reward optimality criterion. The decomposition theory, in Ross and Varadarajan [11], leads to a natural partition of the state space into strongly communicating classes and a set of states...