Mustafa C. Pinar 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
Inspired by an algorithm due to Minieka, 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 it is assigned to. After a lower bounding phase, the algorithm iteratively sets … Read more
Motivated by telecommunication applications, we investigate the shortest path problem on directed acyclic graphs under arc length uncertainties represented as interval numbers. Using a minimax-regret criterion we define and identify robust paths via mixed-integer programming and exploiting interesting structural properties of the problem. Citation Bilkent University, Department of Industrial Engineering, Technical Report August 2001 Article … Read more
The paper proposes a constrained Nonlinear Programming methodology for volatility estimation with GARCH models. These models are usually developed and solved as unconstrained optimization problems whereas they actually fit into nonlinear, nonconvex problems. Computational results on FTSE 100 and S & P 500 indices with up to 1500 data points are given and contrasted to … Read more
For a set of financial securities specified by their expected returns and variance/covariances we propose the concept of minimum risk arbitrage, characterize conditions under which such opportunities may exist. We use conic duality and convex analysis to derive these characterizations. For practical computation a decidability result on the existence of an arbitrage opportunity is derived. … Read more