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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 ..."
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Cited by 522 (19 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
The Nash Bargaining Solution in Economic Modeling
 Rand Journal of Economics
, 1986
"... This article establishes the relationship between the static axiomatic theory of bargaining and the sequential strategic approach to bargaining. We consider two strategic models of alternating offers. The models differ in the source of the incentive of the bargaining parties to reach agreement: the ..."
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Cited by 553 (1 self)
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: the bargainers ' time preference and the risk of breakdown of negotiation. Each of the models has a unique perfect equilibrium. When the motivation to reach agreement is made negligible, in each model the unique perfect equilibrium outcome approaches the Nash bargaining solution, with utilities that reflect
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
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Cited by 552 (10 self)
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that for large n, and for all Φ’s except a negligible fraction, the following property holds: For every y having a representation y = Φα0 by a coefficient vector α0 ∈ R m with fewer than ρ · n nonzeros, the solution α1 of the ℓ 1 minimization problem min �x�1 subject to Φα = y is unique and equal to α0
USER’S GUIDE TO VISCOSITY SOLUTIONS OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS
, 1992
"... The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking argume ..."
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Cited by 1374 (16 self)
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The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking
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 2694 (61 self)
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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
Inverse Acoustic and Electromagnetic Scattering Theory, Second Edition
, 1998
"... Abstract. This paper is a survey of the inverse scattering problem for timeharmonic acoustic and electromagnetic waves at fixed frequency. We begin by a discussion of “weak scattering ” and Newtontype methods for solving the inverse scattering problem for acoustic waves, including a brief discussi ..."
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Cited by 1051 (45 self)
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discussion of Tikhonov’s method for the numerical solution of illposed problems. We then proceed to prove a uniqueness theorem for the inverse obstacle problems for acoustic waves and the linear sampling method for reconstructing the shape of a scattering obstacle from far field data. Included in our
A tutorial on support vector machines for pattern recognition
 Data Mining and Knowledge Discovery
, 1998
"... The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and nonseparable data, working through a nontrivial example in detail. We describe a mechanical analogy, and discuss when SV ..."
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Cited by 3313 (12 self)
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SVM solutions are unique and when they are global. We describe how support vector training can be practically implemented, and discuss in detail the kernel mapping technique which is used to construct SVM solutions which are nonlinear in the data. We show how Support Vector machines can have very
Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach
 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION
, 1999
"... Evolutionary algorithms (EA’s) are often wellsuited for optimization problems involving several, often conflicting objectives. Since 1985, various evolutionary approaches to multiobjective optimization have been developed that are capable of searching for multiple solutions concurrently in a singl ..."
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Cited by 789 (22 self)
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introduce a new evolutionary approach to multicriteria optimization, the Strength Pareto EA (SPEA), that combines several features of previous multiobjective EA’s in a unique manner. It is characterized by a) storing nondominated solutions externally in a second, continuously updated population, b
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 ..."
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Cited by 1373 (16 self)
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to recover f exactly from the data y? We prove that under suitable conditions on the coding matrix A, the input f is the unique solution to the ℓ1minimization problem (‖x‖ℓ1:= i xi) min g∈R n ‖y − Ag‖ℓ1 provided that the support of the vector of errors is not too large, ‖e‖ℓ0: = {i: ei ̸= 0}  ≤ ρ · m
Results 1  10
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