A method of analytic centers for quadratically constrained convex quadratic programs
SIAM Journal on Numerical Analysis
On the convergence of the method of analytic centers when applied to convex quadratic programs
Mathematical Programming: Series A and B
A new algorithm for minimizing convex functions over convex sets
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Computing the Shortest Network under a Fixed Topology
IEEE Transactions on Computers
Journal of Global Optimization
Heuristic solution of the multisource Weber problem as a p-median problem
Operations Research Letters
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The Euclidean multi-facility location (EMFL) problem is one of locating new facilities in the Euclidean space with respect to existing facilities. The problem consists of finding locations of new facilities which will minimize a total cost function which consists of a sum of costs directly proportional to the Euclidean distances between the new facilities, and costs directly proportional to the Euclidean distances between new and existing facilities. In this paper, it is shown that the dual of EMFL proposed by Francis and Cabot is equivalent to the maximization of a linear function subject to convex quadratic inequality constraints and therefore can be solved in polynomial time by interior point methods. We also establish a theorem on the duality gap and present a procedure for recovering the primal solution from an interior dual feasible solution.