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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

2019
*
Notices of the American Mathematical Society
*

In practical computations,

doi:10.1090/noti1776
fatcat:i36w7gkf3fcv7mbpizfkfwu3ki
*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] ). ...##
###
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. ...

##
###
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)

1987
*
Annual Review of Computer Science
*

4 review some

doi:10.1146/annurev.cs.02.060187.001003
fatcat:2bv2mgpyvnhwlf5xfo6yu5jary
*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 ...##
###
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*.) ...

##
###
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

2000
*
Journal of Computational and Applied Mathematics
*

The modern era of

doi:10.1016/s0377-0427(00)00433-7
fatcat:kwhchrvwcncsvmkd7cdjy3wpny
*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. ...##
###
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

1996
*
Mathematical programming
*

It is shown that the iterates

doi:10.1007/bf02592088
fatcat:rxsbar2gsffwlehtaqsn6nmccq
*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. ...##
###
An extension of an interior-point method for entropy minimization

1999
*
1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258)
*

The paper presents

doi:10.1109/icassp.1999.756320
dblp:conf/icassp/Gorodnitsky99
fatcat:zovzzmh25bc4xn7ey3bcpnu66e
*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). ...##
###
Primal-dual interior-point methods
[chapter]

2010
*
Polyhedral and Semidefinite Programming Methods in Combinatorial Optimization
*

The modern era of

doi:10.1090/fim/027/04
fatcat:ps2izalopfhetgouzqqjcy7oti
*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. ...##
###
Primal-Dual Relationship Between Levenberg–Marquardt and Central Trajectories for Linearly Constrained Convex Optimization

2013
*
Journal of Optimization Theory and Applications
*

Our main theorem is particularly relevant in quadratic

doi:10.1007/s10957-013-0492-4
fatcat:yauqgjx6yvf2xbsf5vkd7wfhtm
*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 ...
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