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989,902
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 548 (12 self)
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to SDP. Next we present an interior point algorithm which converges to the optimal solution in polynomial time. The approach is a direct extension of Ye's projective method for linear programming. We also argue that most known interior point methods for linear programs can be transformed in a
INTERIORPOINT LINEAR PROGRAMMING SOLVERS
, 2009
"... A We present an overview of available software for solving linear programming problems using interiorpoint methods. Some of the codes discussed include primal and dual simplex solvers as well, but we focus the discussion on the implementation of the interiorpoint solver. For each solver, we presen ..."
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A We present an overview of available software for solving linear programming problems using interiorpoint methods. Some of the codes discussed include primal and dual simplex solvers as well, but we focus the discussion on the implementation of the interiorpoint solver. For each solver, we
Recent Developments In InteriorPoint Methods
, 1999
"... The modern era of interiorpoint 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 as convex quadrati ..."
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Cited by 3 (1 self)
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The modern era of interiorpoint 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 as convex
On The Symmetric Formulation Of InteriorPoint Methods
, 1994
"... . We present a unified framework for studying interior point methods for linear programming. Within this framework, we compare three fundamental methods: (1) pathfollowing, (2) barrier, and (3) primal/dual affinescaling (our terminology differs slightly from the commonly accepted terminology). The ..."
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Cited by 3 (0 self)
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. We present a unified framework for studying interior point methods for linear programming. Within this framework, we compare three fundamental methods: (1) pathfollowing, (2) barrier, and (3) primal/dual affinescaling (our terminology differs slightly from the commonly accepted terminology
ATOMIC DECOMPOSITION BY BASIS PURSUIT
, 1995
"... The TimeFrequency and TimeScale communities have recently developed a large number of overcomplete waveform dictionaries  stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods for d ..."
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Cited by 2725 (61 self)
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successfully only because of recent advances in linear programming by interiorpoint methods. We obtain reasonable success with a primaldual logarithmic barrier method and conjugategradient solver.
Progress in Linear Programming: InteriorPoint Algorithms
, 1994
"... Abstract: According to current estimates, more than $100 million in human and computer time is invested yearly in the formulation and solution of linear programming problems. Businesses, large and small, use linear programming models to optimize communication systems, to schedule transportation netw ..."
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networks, to control inventories, to plan investments, and to maximize production.... In this article we describe some recent developments in linear programming. We highlight progress in interiorpoint algorithms during the last ten years.
Stability Of Linear Equations Solvers In InteriorPoint Methods
 SIAM J. Matrix Anal. Appl
, 1994
"... . Primaldual interiorpoint methods for linear complementarity and linear programming problems solve a linear system of equations to obtain a modified Newton step at each iteration. These linear systems become increasingly illconditioned in the later stages of the algorithm, but the computed steps ..."
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Cited by 17 (2 self)
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. Primaldual interiorpoint methods for linear complementarity and linear programming problems solve a linear system of equations to obtain a modified Newton step at each iteration. These linear systems become increasingly illconditioned in the later stages of the algorithm, but the computed
Fast linear iterations for distributed averaging.
 Systems & Control Letters,
, 2004
"... Abstract We consider the problem of finding a linear iteration that yields distributed averaging consensus over a network, i.e., that asymptotically computes the average of some initial values given at the nodes. When the iteration is assumed symmetric, the problem of finding the fastest converging ..."
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Cited by 432 (12 self)
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be exploited to speed up interiorpoint methods for solving the fastest distributed linear iteration problem, for networks with up to a thousand or so edges. We also describe a simple subgradient method that handles far larger problems, with up to one hundred thousand edges. We give several extensions
Bundle Adjustment  A Modern Synthesis
 VISION ALGORITHMS: THEORY AND PRACTICE, LNCS
, 2000
"... This paper is a survey of the theory and methods of photogrammetric bundle adjustment, aimed at potential implementors in the computer vision community. Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal structure and viewing parameter estimates. Topics c ..."
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Cited by 562 (13 self)
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covered include: the choice of cost function and robustness; numerical optimization including sparse Newton methods, linearly convergent approximations, updating and recursive methods; gauge (datum) invariance; and quality control. The theory is developed for general robust cost functions rather than
Results 1  10
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989,902