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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.  ... 
doi:10.1016/0024-3795(91)90282-2 fatcat:c2icscvnqbagjiyj4lbw5vbooe

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

Renato D. C. Monteiro, Ilan Adler
1989 Mathematical programming  
We describe a 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.  ... 
doi:10.1007/bf01587076 fatcat:y5dhxnvm45enpozu5vdeonlwou

Algorithms for the solution of quadratic knapsack problems

Panos M. Pardalos, Yinyu Ye, Chi-Geun Han
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  ... 
doi:10.1016/0024-3795(91)90267-z fatcat:jatxtcvdbjcudpd3gaxwzmmsrm

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

Renato D. C. Monteiro, Ilan Adler
1989 Mathematical programming  
We describe a 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.  ... 
doi:10.1007/bf01587075 fatcat:tizxyxqydbcyljzhhbrexprg44

Line Search Techniques for the Logarithmic Barrier Function in Quadratic Programming

M. Ben-Daya
1995 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.  ...  for convex quadratic programming.  ... 
doi:10.1057/jors.1995.47 fatcat:warpm2msvfda5ltlt5lbjvawgi

Path-Following Methods for Linear Programming

Clovis C. Gonzaga
1992 SIAM Review  
In this paper a unified treatment of 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).  ... 
doi:10.1137/1034048 fatcat:vrmdbdp2rvc4pegjj4r52owqma

A randomized scheme for speeding up algorithms for linear and convex programming problems with high constraints-to-variables ratio

Ilan Adler, Ron Shamir
1993 Mathematical programming  
In particular, we give a randomized 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.  ... 
doi:10.1007/bf01582137 fatcat:hgyhifmdyzcv3lcagpta6d6v6u

A polynomial-time algorithm for a class of linear complementarity problems

Masakazu Kojima, Shinji Mizuno, Akiko Yoshise
1989 Mathematical programming  
Under the assumption that M is positive semidefinite, this paper presents 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.  ... 
doi:10.1007/bf01587074 fatcat:rdutagd4xja27idamsjdqodvwe

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  ... 

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.  ... 

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.  ...