OSPF Routing with Optimal Oblivious Performance Ratio Under Polyhedral Demand Uncertainty

We study the best OSPF style routing problem in telecommunication networks, where weight management is employed to get a routing configuration with the minimum oblivious ratio. We consider polyhedral demand uncertainty: the set of traffic matrices is a polyhedron defined by a set of linear constraints, and the performance of each routing is assessed on … Read more

Robust DWDM Routing and Provisioning under Polyhedral Demand Uncertainty

We present mixed integer linear programming models that are robust in the face of uncertain traffic demands known to lie in a certain polyhedron for the problem of dense wavelength division multiplexing network routing and provisioning at minimal cost. We investigate the solution of the problem in a set of numerical experiments for two models … Read more

Provisioning Virtual Private Networks under traffic uncertainty

We investigate a network design problem under traffic uncertainty which arises when provisioning Virtual Private Networks (VPNs): given a set of terminals that must communicate with one another, and a set of possible traffic matrices, sufficient capacity has to be reserved on the links of the large underlying public network so as to support all … Read more

Robust Profit Opportunities in Risky Financial Portfolios

For risky financial securities with given expected return vector and covariance matrix, we propose the concept of a robust profit opportunity in single and multiple period settings. We show that the problem of finding the “most robust” profit opportunity can be solved as a convex quadratic programming problem, and investigate its relation to the Sharpe … Read more

An Exact Algorithm for the Capacitated Vertex p-Center Problem

We develop a simple and practical exact algorithm for the problem of locating $p$ facilities and assigning clients to them within capacity restrictions in order to minimize the maximum distance between a client and the facility to which it is assigned (capacitated $p$-center). The algorithm iteratively sets a maximum distance value within which it tries … Read more

On Robust 0-1 Optimization with Uncertain Cost Coefficients

Based on the recent approach of Bertsimas and Sim \cite{bs1, bs2} to robust optimization in the presence of data uncertainty, we prove a bound on the probability that the robust solution gives an objective function value worse than the robust objective function value, under the assumption that only cost coefficients are subject to uncertainty. A … Read more

An Efficient Exact Algorithm for the Vertex hBcCenter Problem and Computational Experiments for Different Set Covering Subproblems

We develop a simple and yet very efficient exact algorithm for the problem of locating $p$ facilities and assigning clients to them in order to minimize the maximum distance between a client and the facility to which it is assigned. The algorithm iteratively sets a maximum distance value within which it tries to assign all … Read more

Sufficient Global Optimality Conditions for Bivalent Quadratic Optimization

We prove a sufficient global optimality condition for quadratic optimization with quadratic constraints where the variables are allowed to take -1 and 1 values. We extend the condition to quadratic programs with matrix variables and orthogonality conditions, and in particular, to the quadratic assignment problem. Citation Bilkent University Technical Report, September 2002. Article Download View … Read more

Linear Huber M-Estimator under Ellipsoidal Data Uncertainty

The purpose of this note is to present a robust counterpart of the Huber estimation problem in the sense of Ben-Tal and Nemirovski when the data elements are subject to ellipsoidal uncertainty. The robust counterparts are polynomially solvable second-order cone programs with the strong duality property. We illustrate the effectiveness of the robust counterpart approach … Read more

Mesh Topology Design in Overlay Virtual Private Networks

We study the mesh topology design problem in overlay virtual private networks. Given a set of customer nodes and associated traffic matrix, tunnels that are connecting node pairs through a public service provider network subject to degree constraints are determined so as to minimize total multihopped traffic. Valid inequalities strengthening the LP relaxation and a … Read more