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Global Optimization with Polynomials and the Problem of Moments
 SIAM Journal on Optimization
, 2001
"... We consider the problem of finding the unconstrained global minimum of a realvalued polynomial p(x) : R R, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear mat ..."
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Cited by 569 (47 self)
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matrix inequality (LMI) problems. A notion of KarushKuhnTucker polynomials is introduced in a global optimality condition. Some illustrative examples are provided. Key words. global optimization, theory of moments and positive polynomials, semidefinite programming AMS subject classifications. 90C22
Working with the “convex ” KarushKuhnTucker theorem ∗
"... We recall the KarushKuhnTucker theorem for convex programming, as treated in the previous lecture (see Corollary 3.5 of [OSC]). Theorem 1.1 (KarushKuhnTucker) Let f, g1,..., gm: R n → (−∞, +∞] be convex functions, let S ⊂ R n be a convex set. Also, let A be an p × nmatrix and let b ∈ R p. Defin ..."
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We recall the KarushKuhnTucker theorem for convex programming, as treated in the previous lecture (see Corollary 3.5 of [OSC]). Theorem 1.1 (KarushKuhnTucker) Let f, g1,..., gm: R n → (−∞, +∞] be convex functions, let S ⊂ R n be a convex set. Also, let A be an p × nmatrix and let b ∈ R p
Duality and the “convex ” KarushKuhnTucker theorem
"... Our approach to the KarushKuhnTucker theorem in [OSC] was entirely based on subdifferential calculus (essentially, it was an outgrowth of the two subdifferential calculus rules contained in the FenchelMoreau and DubovitskiiMilyutin theorems, i.e., Theorems 2.9 and 2.17 of [OSC]). On the other ha ..."
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Cited by 1 (1 self)
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Our approach to the KarushKuhnTucker theorem in [OSC] was entirely based on subdifferential calculus (essentially, it was an outgrowth of the two subdifferential calculus rules contained in the FenchelMoreau and DubovitskiiMilyutin theorems, i.e., Theorems 2.9 and 2.17 of [OSC]). On the other
A training algorithm for optimal margin classifiers
 PROCEEDINGS OF THE 5TH ANNUAL ACM WORKSHOP ON COMPUTATIONAL LEARNING THEORY
, 1992
"... A training algorithm that maximizes the margin between the training patterns and the decision boundary is presented. The technique is applicable to a wide variety of classifiaction functions, including Perceptrons, polynomials, and Radial Basis Functions. The effective number of parameters is adjust ..."
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Cited by 1848 (44 self)
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A training algorithm that maximizes the margin between the training patterns and the decision boundary is presented. The technique is applicable to a wide variety of classifiaction functions, including Perceptrons, polynomials, and Radial Basis Functions. The effective number of parameters
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 557 (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
Training Support Vector Machines: an Application to Face Detection
, 1997
"... We investigate the application of Support Vector Machines (SVMs) in computer vision. SVM is a learning technique developed by V. Vapnik and his team (AT&T Bell Labs.) that can be seen as a new method for training polynomial, neural network, or Radial Basis Functions classifiers. The decision sur ..."
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Cited by 728 (1 self)
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We investigate the application of Support Vector Machines (SVMs) in computer vision. SVM is a learning technique developed by V. Vapnik and his team (AT&T Bell Labs.) that can be seen as a new method for training polynomial, neural network, or Radial Basis Functions classifiers. The decision
LIBSVM: a Library for Support Vector Machines
, 2001
"... LIBSVM is a library for support vector machines (SVM). Its goal is to help users can easily use SVM as a tool. In this document, we present all its implementation details. 1 ..."
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Cited by 6287 (82 self)
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LIBSVM is a library for support vector machines (SVM). Its goal is to help users can easily use SVM as a tool. In this document, we present all its implementation details. 1
Results 1  10
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