An efficient Newton barrier method for minimizing a sum of Euclidean norms

SIAM Journal on Optimization

Volumn 6, Issue 1, 1996, Pages 74-95

  Andersen, Knud D ^a  

^a UNIVERSITY OF SOUTHERN DENMARK   (Denmark)

Author keywords

Duality; Newton barrier method; Nonsmooth optimization; Sum of norms

Indexed keywords

EID: 0030304772     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/0806006     Document Type: Article

References (29)

1. K. ANDERSEN, An infeasible dual affine scaling method for linear programming, COAL Bulletin, 22 (1993), pp. 19-27.
2. K. ANDERSEN AND E. CHRISTIANSEN, Limit Analysis with the Dual Affine Scaling Algorithm, Preprint 26, Dept. Of Math, and Computer Sci., Odense University, 1993, J. Comput. Applied Math., to appear.
3. C. ASHCRAFT, R. GRIMES, J. LEWIS, B. PEYTON, AND H. SIMON, Progress in sparse matrix methods for large scale linear systems on vector supercomputers, Internat. J. Supercomputer Appl., 1 (1987), pp. 10-30.
4. M. BAZARAA, H. SHERALI, AND C. SHETTY, Nonlinear Programming: Theory and Algorithms, 2nd ed., John Wiley and Sons, New York, 1993.
5. P. CALAMAI AND A. CONN, A second-order method for solving the continuous multifacility location problem, in Numerical Analysis: Proceedings of the Ninth Biennial Conference, Dundee, Scotland, Lecture Notes in Mathematics 912, G. Watson, ed., Berlin, 1982, Springer-Verlag, pp. 1-5.
6. p norm location problems, Math. Programming, 38 (1987), pp. 75-109.
7. E. CHRISTIANSEN AND K. KORTANEK, Computation of the collapse state in limit analysis using the lp primal affine scaling algorithm, J. Comput. Appl. Math., 34 (1991), pp. 47-63.
8. E. CHRISTIANSEN AND S. LARSEN, Computations in limit analysis for plastic plates, Internat. J. Numer. Methods Engrg., 19 (1983), pp. 169-184.
9. U. ECKHARDT, On an Optimization Problem Related to Minimal Surfaces with Obstacles, in Optimization and Optimal Control, Lecture Notes in Mathematics 477, A. Dold and B. Eckmann, eds., Springer-Verlag, 1975, pp. 95-101.
10. J. EYSTER, J. WHITE, AND W. WIERWILLE, On solving multifacility location problems using a hyperboloid approximation procedure, AIIE Trans., 5 (1973), pp. 1-6.
11. A. FIACCO AND G. MCCORMICK, Nonlinear Programming: Sequential Unconstrained Minimization Techniques, John Wiley and Sons, New York, 1968.
12. J. FORREST AND J. TOMLIN, Vector processing in simplex and interior methods for linear programming, Ann. Oper. Res., 22 (1990), pp. 71-100.
13. K. FRISCH, The logarithmic potential method of convex programming, Tech. report, University Institute of Economics, Oslo, Norway, 1955.
14. V. GAUDRAT, A Newton type algorithm for plastic limit analysis, Comput. Methods Appl. Mech. Engrg., 88 (1991), pp. 207-224.
15. A. GEORGE AND J.W.-H. Liu, Computing Solution of Large Sparse Positive Definite Systems, Prentice-Hall, Englewood Cliffs, NJ, 1981.
16. P. GILL, W. MURRAY, M. SAUNDERS, J. TOMLIN, AND M. WRIGHT, On the projected Newton barrier methods for linear programming and an equivalence to Karmarkar's projective method, Math. Programming, 36 (1986), pp. 183-209.
17. H. KUHN, On a pair of dual nonlinear programs, in Nonlinear Programming, J. Abadie, ed., North-Holland, Amsterdam, 1967, pp. 38-54.
18. H. W. KUHN, A note on Fermat's problem, Math. Programming, 4 (1973), pp. 98-107.
19. p problems, SIAM J. Optim., 3 (1993), pp. 609-629.
20. J. LIU, Modification of the minimum-degree algorithm by multiple elimination, ACM Trans. Math. Software, 11 (1985), pp. 141-153.
21. I. LUSTIG R. MARSTEN, AND D. SHANNO, Interior point methods for linear programming: Computational state of the art, Technical report SOR 92-17, Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ, 1992.
22. N. MEGIDDO, Pathways to the optimal set in linear programming, in Progress in Mathematical Programming: Interior-Point Algorithms and Related Methods, N. Megiddo, ed., Springer-Verlag, 1989, pp. 131-158.
23. S. MEHROTRA, On the implementation of a primal-dual interior point method, SIAM J. Optim., 2 (1992), pp. 575-601.
24. M. MINOUX, Mathematical Programming: Theory and Algorithms, John Wiley and Sons, New York, 1986.
25. B. MURTAGH AND M. SAUNDERS, Large-scale linearly constrained optimization, Math. Programming, 14 (1978), pp. 41-72.
26. M. OVERTON, A quadratically convergent method for minimizing a sum of Euclidian norms, Math. Programming, 27 (1983), pp. 34-63.
27. _, Numerical solution of a model problem from collapse load analysis, in INRIA Conf. Comput. Methods Engrg. Appl. Sci., R. Glowinski and J. Lions, eds., North-Holland, Amsterdam, 1984, pp. 421-437.
28. J. RENEGAR, A polynomial-time algorithm, based on Newton's method, for linear programming, Math. Programming, 40 (1988), pp. 59-73.
29. J. ROSEN AND G. XUE, On the convergence of Miehle's algorithm for the Euclidean multifacility location problem, Oper. Res., 40 (1992), pp. 188-191.