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568
Pegasos: Primal Estimated subgradient solver for SVM
"... We describe and analyze a simple and effective stochastic subgradient descent algorithm for solving the optimization problem cast by Support Vector Machines (SVM). We prove that the number of iterations required to obtain a solution of accuracy ɛ is Õ(1/ɛ), where each iteration operates on a singl ..."
Abstract

Cited by 542 (20 self)
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We describe and analyze a simple and effective stochastic subgradient descent algorithm for solving the optimization problem cast by Support Vector Machines (SVM). We prove that the number of iterations required to obtain a solution of accuracy ɛ is Õ(1/ɛ), where each iteration operates on a
A Duality Model of TCP and Queue Management Algorithms
 IEEE/ACM Trans. on Networking
, 2002
"... We propose a duality model of congestion control and apply it to understand the equilibrium properties of TCP and active queue management schemes. Congestion control is the interaction of source rates with certain congestion measures at network links. The basic idea is to regard source rates as p ..."
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Cited by 307 (37 self)
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as primal variables and congestion measures as dual variables, and congestion control as a distributed primaldual algorithm carried out over the Internet to maximize aggregate utility subject to capacity constraints. The primal iteration is carried out by TCP algorithms such as Reno or Vegas
Monotonicity of primaldual interiorpoint algorithms for semidefinite programming problems
, 1998
"... We present primaldual interiorpoint algorithms with polynomial iteration bounds to find approximate solutions of semidefinite programming problems. Our algorithms achieve the current best iteration bounds and, in every iteration of our algorithms, primal and dual objective values are strictly imp ..."
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Cited by 216 (35 self)
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We present primaldual interiorpoint algorithms with polynomial iteration bounds to find approximate solutions of semidefinite programming problems. Our algorithms achieve the current best iteration bounds and, in every iteration of our algorithms, primal and dual objective values are strictly
Probing the Pareto frontier for basis pursuit solutions
, 2008
"... The basis pursuit problem seeks a minimum onenorm solution of an underdetermined leastsquares problem. Basis pursuit denoise (BPDN) fits the leastsquares problem only approximately, and a single parameter determines a curve that traces the optimal tradeoff between the leastsquares fit and the ..."
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Cited by 365 (5 self)
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on this curve; the algorithm is suitable for problems that are large scale and for those that are in the complex domain. At each iteration, a spectral gradientprojection method approximately minimizes a leastsquares problem with an explicit onenorm constraint. Only matrixvector operations are required
INTERIOR PATH FOLLOWING PRIMALDUAL ALGORITHMS. PART I: LINEAR PROGRAMMING
, 1989
"... We describe a primaldual interior point algorithm for linear programming problems which requires a total of O(~fnL) number of iterations, where L is the input size. Each iteration updates a penalty parameter and finds the Newton direction associated with the KarushKuhnTucker system of equations w ..."
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Cited by 199 (11 self)
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We describe a primaldual interior point algorithm for linear programming problems which requires a total of O(~fnL) number of iterations, where L is the input size. Each iteration updates a penalty parameter and finds the Newton direction associated with the KarushKuhnTucker system of equations
Iterative Combinatorial Auctions: Theory and Practice
, 2000
"... Combinatorial auctions, which allow agents to bid directly for bundles of resources, are necessary for optimal auctionbased solutions to resource allocation problems with agents that have nonadditive values for resources, such as distributed scheduling and task assignment problems. We introduc ..."
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Cited by 191 (25 self)
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introduce iBundle, the first iterative combinatorial auction that is optimal for a reasonable agent bidding strategy, in this case myopic bestresponse bidding. Its optimality is proved with a novel connection to primaldual optimization theory. We demonstrate orders of magnitude performance
Primality Test In Iterated Ore Extensions
"... this paper we generalize this test for completely prime ideals in a wide class of iterated Ore extensions of a field. There are interesting examples of algebras where all prime ideals are completely prime. The classical example, the universal enveloping algebra of a finite dimensional solvable Lie a ..."
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Cited by 1 (0 self)
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this paper we generalize this test for completely prime ideals in a wide class of iterated Ore extensions of a field. There are interesting examples of algebras where all prime ideals are completely prime. The classical example, the universal enveloping algebra of a finite dimensional solvable Lie
Primal Methods
"... data • Inputs are feature vectors with class labels {−1, +1} f(x) ≈ y ∀x D = {(x1,y1),..., (xn,yn)} xi ∈ R d Kernel support vector machines • Class boundary is often nonlinear in the original feature space • Project into a higher (possibly infinite) dimensional, nonlinear feature space Dual Decom ..."
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Decomposition Methods Dual optimization • Allows "kernel trick": inputs only appear in dot products • Solving directly requires kernel matrix Working set decomposition • Fast convergence and small memory footprint • Iteratively solve small "working set " of dual variables • Only small kernel
Primal and Dual Interface Concentrated Iterative Substructuring Methods
, 2007
"... This paper is devoted to the fast solution of interface concentrated finite element equations. The interface concentrated finite element schemes are constructed on the basis of a nonoverlapping domain decomposition where a conforming boundary concentrated finite element approximation is used in eve ..."
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Cited by 5 (3 self)
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, and the spatial dimension, respectively. We propose and analyze primal and dual substructuring iterative methods which asymptotically exhibit the same or at least almost the same complexity as the number of unknowns. In particular, the socalled AllFloating Finite Element Tearing and Interconnecting solvers
FETIDPH: a dualprimal domain decomposition method for acoustic scattering,”
 Journal of Computational Acoustics,
, 2005
"... A dualprimal variant of the FETIH domain decomposition method is designed for the fast, parallel, iterative solution of largescale systems of complex equations arising from the discretization of acoustic scattering problems formulated in bounded computational domains. The convergence of this ite ..."
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Cited by 107 (10 self)
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A dualprimal variant of the FETIH domain decomposition method is designed for the fast, parallel, iterative solution of largescale systems of complex equations arising from the discretization of acoustic scattering problems formulated in bounded computational domains. The convergence
Results 1  10
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568