This paper deals with the stability of the intersection of a given set <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$ X\subset \mathbb{R}^{n}$$</EquationSource> </InlineEquation>with the solution, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$F\subset \mathbb{R}^{n}$$</EquationSource> </InlineEquation>, of a given linear system whose coefficients can be arbitrarily perturbed. In the optimization context, the fixed constraint set X can be the...</equationsource></inlineequation></equationsource></inlineequation>

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:<Equation ID="Equ1"> <EquationSource Format="TEX"/> </Equation> We assume these problems to be randomly generated according to the Rotation-Symmetry-Model: *Let a <Subscript>1</Subscript>,…,a <Subscript>m</Subscript>, v be distributed independently,...</subscript></subscript></equation>

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 <Subscript>1</Subscript>,S <Subscript>2</Subscript>,… , S <Subscript>N</Subscript>. The servers have different rates. The service times at each server are independent and exponentially distributed....</subscript></subscript></subscript>

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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${O(r^{3/2}\,\log\epsilon^{-1})}$$</EquationSource> </InlineEquation> for the NT methods,...</equationsource></inlineequation>

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 <Superscript>T</Superscript>x ≤ β}, the algorithm finds a...</superscript>

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...

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...