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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 1399 (16 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 860 (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
Adjustable robust solutions of uncertain linear programs
, 2004
"... 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 370 (12 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
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 482 (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
 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
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 ..."
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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 788 (30 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.
The linear programming approach to approximate dynamic programming
 Operations Research
, 2001
"... The curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of largescale stochastic control problems. We study an efficient method based on linear programming for approximating solutions to such problems. The approach “fits ” a linear ..."
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Cited by 225 (16 self)
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The curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of largescale stochastic control problems. We study an efficient method based on linear programming for approximating solutions to such problems. The approach “fits ” a linear
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