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Page 2926 of Mathematical Reviews Vol. , Issue 92e [page]

1992 Mathematical Reviews  
Programming 51 (1991), no. 1, (Ser. A), 17-43. Summary: “We present a new projective interior point method for linear programming with unknown optimal value.  ...  The author considers interior-point methods for linear programs.  ... 

Page 1344 of Mathematical Reviews Vol. , Issue 97B [page]

1997 Mathematical Reviews  
of path-following methods in linear programming.  ...  (CH-GENV-ID; Geneva) Primal-dual target-following algorithms for linear programming. (English summary) Interior point methods in mathematical programming. Ann. Oper. Res. 62 (1996), 197-231.  ... 

Algebraic, Geometric, and Topological Methods in Optimization

Jesús A. De Loera
2019 Notices of the American Mathematical Society  
In practical computations, interior point methods follow a piecewise-linear approximation to the central path, using Newton methods steps (see e.g., [7] ).  ...  Interior point methods have had a profound impact in modern optimization, and in applications in engineering and science.  ...  In practical computations, interior point methods follow a piecewise-linear approximation to the central path, using Newton methods steps (see e.g., [7] ).  ... 
doi:10.1090/noti1776 fatcat:i36w7gkf3fcv7mbpizfkfwu3ki

Author index for volume 152

1991 Linear Algebra and its Applications  
A Potential-Reduction Variant of Renegar's Short-Step Path-Following Method for Lin- ear Programming, 43 DOMI~, timizing Over Three-Dimensional Sub- spaces in an Interior-Point Method for  ...  .: 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

Page 5785 of Mathematical Reviews Vol. , Issue 93j [page]

1993 Mathematical Reviews  
This article gives an excellent review of those interior point meth- ods for linear programming known as path-following algorithms.  ...  (BR-FRJ-CE) Path-following methods for linear programming. SIAM Rev. 34 (1992), no. 2, 167-224.  ... 

Linear Programming (1986)

N Megiddo
1987 Annual Review of Computer Science  
4 review some methods of nonlinear programming applied to linear programming; and in Section 5 survey recent algorithms for linear programming that involve Newton's method.  ...  If @ does not contain the optimum then there exists a point a(@) in the relative interior of @ with the following property: For every x interior to @ and every c: > 0, if the starting point x0 is sufficiently  ... 
doi:10.1146/annurev.cs.02.060187.001003 fatcat:2bv2mgpyvnhwlf5xfo6yu5jary

Page 2470 of Mathematical Reviews Vol. , Issue 95d [page]

1995 Mathematical Reviews  
The iteration bounds, obtained in the thesis for path-following methods, are in the linear case comparable with the iteration bounds for the other interior point methods.  ...  Finally, in Chapter 5, the relation of path-following methods and other interior point methods is discussed.  ... 

Page 5546 of Mathematical Reviews Vol. , Issue 88j [page]

1988 Mathematical Reviews  
Summary (translated from the Spanish): “We present a projective gradient algorithm for linear programming.  ...  In this method the solution is found by following a gradient path through the interior of the feasible region and through subspaces of reduced dimension corresponding to the bounding hypersurfaces of the  ... 

Progress in mathematical programming

1990 European Journal of Operational Research  
For a presentation of a related interior point algorithm for linear programming based on Newton's method, see [Ren86].  ...  The common feature to most of the new polynomial algorithms is the path-following aspect. The method of McCormick-Sofer for convex programming also follows a path.)  ... 
doi:10.1016/0377-2217(90)90262-a fatcat:gs7on6tmo5ahxnmhx4btkbw6fy

Page 5278 of Mathematical Reviews Vol. , Issue 92i [page]

1992 Mathematical Reviews  
(BR-FRJ-E) Interior point algorithms for linear programming with inequality constraints. Math. Programming 52 (1991), no. 2, Ser. B, 209-225. In the work of N.  ...  The author proposes a new method for solving linear programs by transforming the problem into a linear minimax problem.  ... 

Interior-point methods

Florian A. Potra, Stephen J. Wright
2000 Journal of Computational and Applied Mathematics  
The modern era of interior-point methods dates to 1984, when Karmarkar proposed his algorithm for linear programming.  ...  We review some of the key developments in the area, and include comments on the complexity theory and practical algorithms for linear programming, semi-deÿnite programming, monotone linear complementarity  ...  We are grateful to an anonymous referee for a speedy but thorough review.  ... 
doi:10.1016/s0377-0427(00)00433-7 fatcat:kwhchrvwcncsvmkd7cdjy3wpny

An $$O(\sqrt n L)$$ iteration bound primal-dual cone affine scaling algorithm for linear programmingiteration bound primal-dual cone affine scaling algorithm for linear programming

Jos F. Sturm, Shuzhong Zhang
1996 Mathematical programming  
It is shown that the iterates follow the primal-dual central path in a neighbourhood larger than the conventional ./K 2 neighbourhood.  ...  In this paper we introduce a primal-dual affine scaling method. The method uses a search-direction obtained by minimizing the duality gap over a linearly transformed conic section.  ...  Jan Brinkhuis for providing us an elegant proof for Lemma 5. I.  ... 
doi:10.1007/bf02592088 fatcat:rxsbar2gsffwlehtaqsn6nmccq

An extension of an interior-point method for entropy minimization

I.F. Gorodnitsky
1999 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258)  
The paper presents a novel algorithm for entropy optimization. The algorithm is motivated by the efficient interior-point methods developed in Linear Programming.  ...  I show that for some entropy functions the proposed algorithm has superior convergence properties when compared to comparable the interior-point methods.  ...  Much of this advance in Linear Programming has been associated with the development of interior-point methods (IMPS).  ... 
doi:10.1109/icassp.1999.756320 dblp:conf/icassp/Gorodnitsky99 fatcat:zovzzmh25bc4xn7ey3bcpnu66e

Primal-dual interior-point methods [chapter]

2010 Polyhedral and Semidefinite Programming Methods in Combinatorial Optimization  
The modern era of interior-point methods dates to 1984, when Karmarkar proposed his algorithm for linear programming.  ...  In the years since then, algorithms and software for linear programming have become quite sophisticated, while extensions to more general classes of problems, such a s c o n vex quadratic programming,  ...  We are grateful to an anonymous referee for a speedy but thorough review.  ... 
doi:10.1090/fim/027/04 fatcat:ps2izalopfhetgouzqqjcy7oti

Primal-Dual Relationship Between Levenberg–Marquardt and Central Trajectories for Linearly Constrained Convex Optimization

Roger Behling, Clovis Gonzaga, Gabriel Haeser
2013 Journal of Optimization Theory and Applications  
Our main theorem is particularly relevant in quadratic programming, where points on the primal-dual L-M trajectory can be calculated by means of a system of linear equations.  ...  We consider the minimization of a convex function on a compact polyhedron defined by linear equality constraints and nonnegative variables.  ...  This work is supported by CNPq and FAPESP (grant 2010/19720-5) from Brazil, The authors would like to thank Professor Yinyu Ye, Luiz Rafael dos Santos and the referees for their contributions to this work  ... 
doi:10.1007/s10957-013-0492-4 fatcat:yauqgjx6yvf2xbsf5vkd7wfhtm
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