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Page 338 of The Journal of the Operational Research Society Vol. 46, Issue 3
[page]

1995
*
The Journal of the Operational Research Society
*

Liu (1991)

*An**O*(*n3L*)*primal**interior**point**algorithm**for**convex**quadratic**programming*. Math. Prog. 49, 325-340. . R. D. C. Monteiro and I. ADLER (1989)*Interior*path following*primal*-dual*algorithms*. ... Suetry (1990) Polynomial barrier function*algorithms**for**convex**quadratic**program*- ming. Arabian. J Sci. and Eng. 15, 657-670. . D. Gotprars and S. ...##
###
Author index for volume 152

1991
*
Linear Algebra and its Applications
*

*O*., Ptwtw, FLORIAN, ANI> YE, YIXYU: On Some Efficient

*Interior*

*Point*Methods

*for*Nonlinear

*Convex*

*Program*- ming, Ifi9 LUSTIC, IRVIN J.. ... .: Computational Experi- ence with a

*Primal*-Dual

*Interior*

*Point*Method

*for*Linear

*Programming*, 191 MAHSTEN, Rou E. See Lustig, Irvin J. ...

##
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Interior path following primal-dual algorithms. part II: Convex quadratic programming

1989
*
Mathematical programming
*

We describe a

doi:10.1007/bf01587076
fatcat:y5dhxnvm45enpozu5vdeonlwou
*primal*-dual*interior**point**algorithm**for**convex**quadratic**programming*problems which requires a total of*O*(~/nL) number of iterations, where L is the input size. ... The*algorithm*is based on the path following idea. The total number of arithmetic operations is shown to be of the order of*O*(*n3L*). ... Acknowledgement The authors wish to thank Michael Todd and two anonymous referees*for*many useful comments. ...##
###
Algorithms for the solution of quadratic knapsack problems

1991
*
Linear Algebra and its Applications
*

*Convex*

*quadratic*

*programming*can be solved in polynomial time using the ellipsoid

*algorithm*or

*an*

*interior*

*point*method. ...

*CONVEX*

*QUADRATIC*KNAPSACK PROBLEMS

*Convex*

*quadratic*

*programming*can be solved in polynomial time using the ellipsoid method iterations and

*O*(

*n3L*> operations. ... Karmarkar, A new polynomial-time

*algorithm*

*for*linear

*programming*, Combinutorica 4:373-395 (1984 ...

##
###
Interior path following primal-dual algorithms. part I: Linear programming

1989
*
Mathematical programming
*

We describe a

doi:10.1007/bf01587075
fatcat:tizxyxqydbcyljzhhbrexprg44
*primal*-dual*interior**point**algorithm**for*linear*programming*problems which requires a total of*O*(~fnL) number of iterations, where L is the input size. ... The*algorithm*is based on the path following idea. ... Acknowledgement The authors wish to thank Michael Todd and two anonymous referees*for*many useful comments and in particular,*for*suggesting some simplifications in the proof of Theorem 4. ...##
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Line Search Techniques for the Logarithmic Barrier Function in Quadratic Programming

1995
*
Journal of the Operational Research Society
*

Liu (1991)

doi:10.1057/jors.1995.47
fatcat:warpm2msvfda5ltlt5lbjvawgi
*An**O*(*n3L*)*primal**interior**point**algorithm**for**convex**quadratic**programming*. Math. Prog. 49, 325-340. . R. D. C. Monteiro and I. ADLER (1989)*Interior*path following*primal*-dual*algorithms*. ...*for**convex**quadratic**programming*. ...##
###
Path-Following Methods for Linear Programming

1992
*
SIAM Review
*

In this paper a unified treatment of

doi:10.1137/1034048
fatcat:vrmdbdp2rvc4pegjj4r52owqma
*algorithms*is described*for*linear*programming*methods based on the central path. ... Polynomial*algorithms*are obtained by following the curve approximately, and this concept becomes precise by using explicit rules*for*measuring the proximity of a*point*in relation to the central path. ... Let (x, z) be*an**interior*feasible pair. (i) Fq(x0, zo) =*O*((qn)L). ...##
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A randomized scheme for speeding up algorithms for linear and convex programming problems with high constraints-to-variables ratio

1993
*
Mathematical programming
*

In particular, we give a randomized

doi:10.1007/bf01582137
fatcat:hgyhifmdyzcv3lcagpta6d6v6u
*algorithm**for*solving*convex**quadratic*and linear*programs*, which uses that scheme together with a variant of Karmarkar's*interior**point*method. ... We extend Clarkson's randomized*algorithm**for*linear*programming*to a general scheme*for*solving*convex*optimization problems. ...*For**convex**quadratic**programming*problems,*an**algorithm*based on Karmarkar's*interior*path method gives a solution in*O*(*n3L*) time (see, e.g., [10] (nd + d4L) ). Proof. ...##
###
A polynomial-time algorithm for a class of linear complementarity problems

1989
*
Mathematical programming
*

Under the assumption that M is positive semidefinite, this paper presents

doi:10.1007/bf01587074
fatcat:rdutagd4xja27idamsjdqodvwe
*an**algorithm*that solves the problem in*O*(n 3 L) arithmetic operations by tracing the path of centers, {(x, y) E S: x~y~ = I.* ... (i = 1, 2,..., n)*for*some/~ > 0} of the feasible region S = {(x, y) >~ 0: y = Mx + q}, where L denotes the size of the input data of the problem. ... We first observe that (x,y) satisfies the Karush-Kuhn-Tucker optimality condition (see,*for*example, [13] ) with a Lagrangian multiplier vector u c R n : y-~X-le+MXu=*O*, x-/xy-le-u=*O*and y-Mx=q. ...##
###
Page 1790 of Mathematical Reviews Vol. 26, Issue Index
[page]

*
Mathematical Reviews
*

., 94i:90088
Goldfarb, Donald (with Liu, Shu Cheng)

*An**O*(*n3L*)*primal*-dual potential reduction*algorithm**for*solving*convex**quadratic**programs*. ... .; Ye, Yinyu) On the solution of indefinite*quadratic*problems using*an**interior*-*point**algorithm*. ...##
###
Page 1748 of Mathematical Reviews Vol. 24, Issue Index
[page]

*
Mathematical Reviews
*

Inertia- controlling methods

*for*general*quadratic**programming*. 92b:90162 Goldfarb, Donald (with Liu, Shu Cheng)*An**O*(*n3L*)*primal**interior**point**algorithm**for**convex**quadratic**programming*. 924:90065 — ... Hamiltonian cycles,*quadratic**programming*, and ranking of extreme*points*. 92m:90052 Filar, Jerzy A. see Chen, Ming, 92m:90052 Hammer, Peter L. see Boros, Endre, 92j:90049 Karmarkar, Narendra*An**interior*-poini ...##
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Page 441 of Mathematical Reviews Vol. 24, Issue Index
[page]

*
Mathematical Reviews
*

(Wilfried Grossmann) 92c:90049 90B10 (90C05)
— (with Liu, Shu Cheng)

*An**O*(*n3L*)*primal**interior**point**algorithm**for**convex**quadratic**programming*. Math.*Programming*49 (1990/91), no. 3, (Ser. ... Azpeitia) 92d:90065 90C20 (65K05) — (with Xiao, Dong) A*primal*projective*interior**point*method*for*linear*programming*. Math.*Programming*51 (1991), no. 1, (Ser. A), 17-43. (B. ...##
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Page 449 of Mathematical Reviews Vol. 26, Issue Index
[page]

*
Mathematical Reviews
*

*Programming*58 (1993), no. 1, Ser. A, 33-52. (S. R. Arora) 94e:90049 90005 — (with Liu, Shu Cheng)

*An*

*O*(

*n3L*)

*primal*-dual potential reduction

*algorithm*

*for*solving

*convex*

*quadratic*

*programs*. ... A path-following projective

*interior*

*point*method

*for*linear

*programming*. (English summary) SIAM J. Optim. 4 (1994), no. 1, 65-85. ...