# Strict Monotonicity and Improved Complexity in the Standard Form Projective Algorithm for Linear-programming

## Primary tabs

Bibliographic reference | Anstreicher, KM.. Strict Monotonicity and Improved Complexity in the Standard Form Projective Algorithm for Linear-programming. In: Mathematical Programming, Vol. 62, no. 3, p. 517-535 (1993) |
---|---|

Permanent URL | http://hdl.handle.net/2078.1/49203 |

## References Provided by I4OC

- K.M. Anstreicher, “A monotonic projective algorithm for fractional linear programming,”Algorithmica 1 (1986a) 483–498.
- K.M. Anstreicher, “A strengthened acceptance criterion for approximate projections in Karmarkar's algorithm,”Operations Research Letters 5 (1986b) 211–214.
- K.M. Anstreicher and R.A. Bosch, “Long steps in an O(n 3 L) algorithm for linear programming,”Mathematical Programming 54 (1992) 251–265.
- K.M. Anstreicher and P. Watteyne, “A family of search directions for Karmarkar's algorithm,” Discussion Paper 9030, Center for Operations Research and Econometrics, Université Catholoque de Louvain (Louvain-la-Neuve, Belgium, 1990).
- G. de Ghellinck and J.-P. Vial, “A polynomial Newton method for linear programming,”Algorithmica 1 (1986) 425–453.
- C. Fraley and J.-P. Vial, “Single-phase versus multi-phase projective methods for linear programming,” COMIN, University of Geneva (Geneva, Switzerland, 1989).
- R.M. Freund, “Projective transformations for interior point methods, part I: basic theory and linear programming,” Working Paper 179-88, OR Center, MIT (Cambridge, MA, 1988).
- R.M. Freund, “Polynomial-time algorithms for linear programming based only on primal scaling and projected gradients of a potential function,”Mathematical Programming 51 (1991) 203–222.
- D.M. Gay, “A variant of Karmarkar's linear programming algorithm for problems in standard form,”Mathematical Programming 37 (1987) 81–90.
- C.C. Gonzaga, “Conical projection algorithms for linear programming,”Mathematical Programming 43 (1989) 151–173.
- C.C. Gonzaga, “Large step path-following methods for linear programming, part I: barrier function method,”SIAM Journal on Optimization 1 (1991a), 268–279.
- C.C. Gonzaga, “Large step path-following methods for linear programming, part II: potential reduction method,”SIAM Journal on Optimization 1 (1991b), 280–292.
- B. Kalantari, “Karmarkar's algorithm with improved steps,”Mathematical Programming 46 (1990), 73–78.
- N. Karmarkar, “A new polynomial-time algorithm for linear programming,”Combinatorica 4 (1984) 373–395.
- M. Padberg, “A different convergence proof of the projective method for linear programming,”Operations Research Letters 4 (1986) 253–257.
- J. Renegar, “A polynomial-time algorithm, based on Newton's method, for linear programming,”Mathematical Programming 40 (1988) 59–93.
- C. Roos and J.-P. Vial, “Long steps with the logarithmic penalty barrier function in linear programming,” in: J. Gabszewicz, J.-F. Richard and L. Wolsey, eds.Economic Decision Making:Games, Econometrics and Optimisation. Contributions in Honour of Jacques H. Drèze (Elsevier, Amsterdam, 1990) pp. 433–441.
- A. Schrijver,Theory of Linear and Integer Programming (Wiley, New York, 1986).
- D. Shaw and D. Goldfarb, “A path-following projective interior point method for linear programming,” (1990), to appear in:SIAM Journal on Optimization.
- A.E. Steger, “An extension of Karmarkar's algorithm for bounded linear programming problems,” M.S. Thesis, State University of New York (Stonybrook, NY, 1985).
- M.J. Todd, “The effect of sparsity, degeneracy, and null and unbounded variables on variants of Karmarkar's linear programming algorithm,” Technical Report 857, School of OR/IE, Cornell University (Ithaca, NY, 1989).
- M.J. Todd and B.P. Burrell, “An extension of Karmarkar's algorithm for linear programming using dual variables,”Algorithmica 1 (1986) 409–424.
- M.J. Todd and Y. Ye, “A centered projective algorithm for linear programming,”Mathematics of Operations Research 15 (1990) 508–529.
- Y. Ye, “A class of projective transformations for linear programming,”SIAM Journal on Computing 19 (1990) 457–466.
- Y. Ye, “An O(n 3 L) potential reduction algorithm for linear programming,”Mathematical Programming 50 (1991) 239–258.
- Y. Ye and M. Kojima, “Recovering optimal solutions in Karmarkar's polynomial algorithm for linear programming,”Mathematical Programming 39 (1987) 305–317.