# Long-step strategies in interior-point primal-dual methods

## Primary tabs

Bibliographic reference | Nesterov, Yurii. Long-step strategies in interior-point primal-dual methods.Faculty Research Seminar on Optimization in Theory and Practice (UNIV IOWA, OBERMANN CTR ADV STUDIES, IOWA CITY
(Ia), Aug 01-12, 1994). In: Mathematical Programming, Vol. 76, no. 1, p. 47-94 (1997) |
---|---|

Permanent URL | http://hdl.handle.net/2078.1/62801 |

## References Provided by I4OC

- D.A. Bayer and J.C. Lagarias, “The nonlinear geometry of linear programming. I: Affine and projective scaling trajectories. II: Legendre transform coordinates and central trajectories,”Transactions of the American Mathematical Society 314 (1989) 499–581.
- G. de Ghellink and J.-P. Vial, “A polynomial Newton method for linear programming,”Algorithmica 1 (1986) 425–453.
- I.I. Dikin, “Iterative solution of problems of linear and quadratic programming,”Soviet Mathematics, Doklady 8 (1967) 674–675.
- C.C. Gonzaga, “An algorithm for solving linear programming problems in O(n 3 L) operations,” in: N. Meggido, ed.,Progress in Mathematical Programming: Interior Point and Related Methods (Springer-Verlag, Berlin, 1989) pp. 1–28.
- C.C. Gonzaga and R.A. Tapia, “On the quadratic convergence of the simplified Mizuno-Todd-Ye algorithm for Linear Programming,” Research Report TR92-42, Rice University, Houston, TX 77 251 (1992).
- B. Jansen, C. Roos, T. Terlaky and J.-P. Vial, “Interior-point methodology for Linear Programming: Duality, sensitivity analysis and computational aspects.” Technical Report No. 1993.12, Geneva University (1993).
- N. Karmarkar, “A new polynomial-time algorithm for linear programming,”Combinatorica 4 (1984) 373–395.
- M. Kojima, N. Meggido, T. Noma and Y. Yoshise, “A unified approach to interior point algorithms for linear complementarity problems,”Lecture Notes in Computer Science, Vol. 538 (Springer-Verlag, New York, 1991).
- S. Mizuno, M.J. Todd and Y. Ye, “On adaptive step primal-dual interior-point algorithms for linear programming,”Mathematics of Operations Research 18 (1993) 964–981.
- Nesterov Yurii, Nemirovskii Arkadii,
*Interior-Point Polynomial Algorithms in Convex Programming*, ISBN:9780898713190, 10.1137/1.9781611970791 - Yu. Nesterov, “Complexity estimates of some cutting plane methods based on analytical barrier,”Mathematical Programming 69 (1995) 149–176.
- J. Renegar, “A polynomial time algorithm, based on Newton’s method, for linear programming,”Mathematical Programming 40 (1988) 59–93.
- K. Tanabe, “Centered Newton method for mathematical programming,” in: M. Iri and K. Yajima, eds.,System Modeling and Optimization: Proceedings of the 13th IFIP Conference. Tokyo, Japan, Aug./Sept. 1987, Vol. 113 ofLecture Notes in Control and Information Sciences (Springer-Verlag, Berlin, 1988) pp. 197–206.
- M.J. Todd and Y. Ye, “A centered projective algorithm for linear programming,”Mathematics of Operations Research 15 (1990) 508–529.
- P.M. Vaidya, “An algorithm for linear programming which requires O(((m + n)n 2 + (m + n)1,5 n)L) arithmetic operations,”Mathematical Programming 47 (1990) 175–202.
- Y. Ye, “An O(n 3 L) potential reduction algorithm for linear programming,”Mathematical Programming 50 (1991) 239–258.