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Decoding by Linear Programming
, 2004
"... This paper considers the classical error correcting problem which is frequently discussed in coding theory. We wish to recover an input vector f ∈ Rn from corrupted measurements y = Af + e. Here, A is an m by n (coding) matrix and e is an arbitrary and unknown vector of errors. Is it possible to rec ..."
Abstract

Cited by 1400 (17 self)
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for some ρ> 0. In short, f can be recovered exactly by solving a simple convex optimization problem (which one can recast as a linear program). In addition, numerical experiments suggest that this recovery procedure works unreasonably well; f is recovered exactly even in situations where a significant
A NEW POLYNOMIALTIME ALGORITHM FOR LINEAR PROGRAMMING
 COMBINATORICA
, 1984
"... We present a new polynomialtime algorithm for linear programming. In the worst case, the algorithm requires O(tf'SL) arithmetic operations on O(L) bit numbers, where n is the number of variables and L is the number of bits in the input. The running,time of this algorithm is better than the ell ..."
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Cited by 848 (3 self)
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We present a new polynomialtime algorithm for linear programming. In the worst case, the algorithm requires O(tf'SL) arithmetic operations on O(L) bit numbers, where n is the number of variables and L is the number of bits in the input. The running,time of this algorithm is better than
Robust solutions to uncertain linear programs
 OR Letters
, 1999
"... We consider linear programs with uncertain parameters, lying in some prescribed uncertainty set, where part of the variables must be determined before the realization of the uncertain parameters (”nonadjustable variables”), while the other part are variables that can be chosen after the realization ..."
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Cited by 358 (15 self)
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We consider linear programs with uncertain parameters, lying in some prescribed uncertainty set, where part of the variables must be determined before the realization of the uncertain parameters (”nonadjustable variables”), while the other part are variables that can be chosen after
Linear Programming: Foundations and Extensions
, 1996
"... under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher. ISBN 0000000000 The text for this book was formated in Time ..."
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Cited by 196 (0 self)
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under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher. ISBN 0000000000 The text for this book was formated in TimesRoman and the mathematics was formated in Michael Spivak’s Mathtimes using AMSL ATEX(which is a macro package for Leslie Lamport’s L ATEX, which itself is a macro package for Donald Knuth’s TEXtext formatting system) and converted from deviceindependent to postscript format using DVIPS. The figures were produced using SHOWCASE on a Silicon Graphics, Inc. workstation and were incorporated into the text as encapsulated postscript files with the macro package called PSFIG.TEX. To my parents, Howard and Marilyn, my dear wife, Krisadee, and the babes, Marisa and Diana Contents
Linear Programming
 in Combinatorial Optimization, Mathematical Programming
, 1994
"... Introduction to Linear Programming Linear programming is a very important class of problems, both algorithmically and combinatorially. Linear programming has many applications. From an algorithmic pointofview, the simplex was proposed in the forties (soon after the war, and was motivated by milit ..."
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Cited by 1 (0 self)
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Introduction to Linear Programming Linear programming is a very important class of problems, both algorithmically and combinatorially. Linear programming has many applications. From an algorithmic pointofview, the simplex was proposed in the forties (soon after the war, and was motivated
Minimax Programs
 University of California Press
, 1997
"... We introduce an optimization problem called a minimax program that is similar to a linear program, except that the addition operator is replaced in the constraint equations by the maximum operator. We clarify the relation of this problem to some betterknown problems. We identify an interesting spec ..."
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Cited by 475 (5 self)
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We introduce an optimization problem called a minimax program that is similar to a linear program, except that the addition operator is replaced in the constraint equations by the maximum operator. We clarify the relation of this problem to some betterknown problems. We identify an interesting
Linear Programming An Introduction to Linear Programming
"... Linear programming is a very important class of problems, both algorithmically and combinatorially. Linear programming has many applications. From an algorithmic pointofview, the simplex was proposed in the forties (soon after the war, and was motivated by military applications) and, although it h ..."
Abstract
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Linear programming is a very important class of problems, both algorithmically and combinatorially. Linear programming has many applications. From an algorithmic pointofview, the simplex was proposed in the forties (soon after the war, and was motivated by military applications) and, although
The Extended Linear Complementarity Problem
, 1993
"... We consider an extension of the horizontal linear complementarity problem, which we call the extended linear complementarity problem (XLCP). With the aid of a natural bilinear program, we establish various properties of this extended complementarity problem; these include the convexity of the biline ..."
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Cited by 776 (28 self)
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We consider an extension of the horizontal linear complementarity problem, which we call the extended linear complementarity problem (XLCP). With the aid of a natural bilinear program, we establish various properties of this extended complementarity problem; these include the convexity
Linear Programming
, 2006
"... This paper is a short didactical introduction to Linear Programming (LP). The main topics are: formulations, notes in convex analysis, geometry of LP, simplex method, duality, ellipsoid algorithm, interior point methods. ..."
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This paper is a short didactical introduction to Linear Programming (LP). The main topics are: formulations, notes in convex analysis, geometry of LP, simplex method, duality, ellipsoid algorithm, interior point methods.
Linear programming in linear time when the dimension is fixed
 J
, 1953
"... Abstract. It is demonstrated hat he linear programming problem in d variables and n constraints can be solved in O(n) time when d is fixed. This bound follows from a multidimensional search technique which is applicable for quadratic programming aswell. There is also developed an algorithm that is p ..."
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Cited by 220 (12 self)
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Abstract. It is demonstrated hat he linear programming problem in d variables and n constraints can be solved in O(n) time when d is fixed. This bound follows from a multidimensional search technique which is applicable for quadratic programming aswell. There is also developed an algorithm
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