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An interior-point method for the single-facility location problem with mixed norms using a conic formulation

Bibliographic reference Chares, Robert ; Glineur, François. An interior-point method for the single-facility location problem with mixed norms using a conic formulation. In: Mathematical Methods of Operations Research, Vol. 68, no. 3, p. 383-405 (Décembre 2008)
Permanent URL http://hdl.handle.net/2078.1/23486
  1. Andersen KD, Christiansen E, Conn AR, Overton ML (2000) An efficient primal–dual interior-point method for minimizing a sum of euclidean norms. SIAM J Sci Comput 22(1): 243–262
  2. Ben-Tal Aharon, Nemirovski Arkadi, Lectures on Modern Convex Optimization : Analysis, Algorithms, and Engineering Applications, ISBN:9780898714913, 10.1137/1.9780898718829
  3. Boyd Stephen, Vandenberghe Lieven, Convex Optimization, ISBN:9780511804441, 10.1017/cbo9780511804441
  4. Carrizosa E, Fliege J (2002) Generalized goal programming: Polynomial methods and applications. Math Programm 93(2): 281–303
  5. del Mar Hershenson M, Boyd SP, Lee TH (2001) Optimal design of a cmos op-amp via geometric programming. IEEE Trans Comput Aided Des Integr Circuits Syst 20(1): 1–21
  6. den Hertog D, Jarre F, Roos C, Terlaky T (1995) A sufficient condition for self-concordance with application to some classes of structured convex programming problems. Math Programm 69: 75–88
  7. Fliege J (2000) Solving convex location problems with gauges in polynomial time. Stud Locat Anal 14: 153–172
  8. Fliege J, Nickel S (2000) An interior point method for multifacility location problems with forbidden regions. Stud Locat Anal 14: 23–46
  9. Glineur F (2001a) Proving strong duality for geometric optimization using a conic formulation. Ann Oper Res 105: 155–184
  10. Glineur F (2001b) Topics in convex optimization: interior-point methods, conic duality and approximations. Ph.D. thesis, Faculté Polytechnique de Mons, Mons, Belgium, January 2001
  11. Glineur F, Terlaky T (2004) Conic formulation for l p -norm optimization. J Optim Theory Appl 122(2): 285–307
  12. Griewank A (2000) Evaluating derivatives: principles and techniques of algorithmic differentiation. Frontiers in applied mathematics, vol 19. SIAM, Philadelphia
  13. Karmarkar N (1984) A new polynomial-time algorithm for linear programming. Combinatorica 4: 373–395
  14. Love RF, Morris JG, Wesolowsky GO (1988) Facilities location: models & methods. North Holland, Amsterdam
  15. Nash S, Sofer A (1998) On the complexity of a practical interior-point method. SIAM J Optim 8(3): 833–849
  16. Nesterov Y (1997) Interior-point methods: An old and new approach to nonlinear programming. Math Programm 79: 285–297
  17. Nesterov Y (2006) Towards nonsymmetric conic optimization. CORE Discussion Paper, 28
  18. Nesterov Yurii, Nemirovskii Arkadii, Interior-Point Polynomial Algorithms in Convex Programming, ISBN:9780898713190, 10.1137/1.9781611970791
  19. Nesterov Y, Todd MJ (1997) Self-scaled barriers and interior-point methods for convex programming. Math Oper Res 22: 1–42
  20. Renegar James, A Mathematical View of Interior-Point Methods in Convex Optimization, ISBN:9780898715026, 10.1137/1.9780898718812
  21. Weiszfeld E (1937) Sur le point par lequel le somme des distances de n points donnés est minimum. Tohoku Math J 4: 355–386
  22. Xue G, Ye Y (1997) An efficient algorithm for minimizing a sum of euclidean norms with applications. SIAM J Optim 7(4): 1017–1036
  23. Xue G, Ye Y (1998) An efficient algorithm for minimizing a sum of p-norms. SIAM J Optim 10(2): 551–579