Results 1 
6 of
6
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 ..."
Abstract

Cited by 1422 (44 self)
 Add to MetaCart
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 adjusted automatically to match the complexity of the problem. The solution is expressed as a linear combination of supporting patterns. These are the subset of training patterns that are closest to the decision boundary. Bounds on the generalization performance based on the leaveoneout method and the VCdimension are given. Experimental results on optical character recognition problems demonstrate the good generalization obtained when compared with other learning algorithms.
Method of centers for minimizing generalized eigenvalues
 Linear Algebra Appl
, 1993
"... We consider the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices, each of which depends affinely on the decision variables. Although this problem may appear specialized, it is in fact quite general, and includes for example all linear, quadratic, and linear fr ..."
Abstract

Cited by 63 (12 self)
 Add to MetaCart
We consider the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices, each of which depends affinely on the decision variables. Although this problem may appear specialized, it is in fact quite general, and includes for example all linear, quadratic, and linear fractional programs. Many problems arising in control theory can be cast in this form. The problem is nondifferentiable but quasiconvex, so methods such as Kelley's cuttingplane algorithm or the ellipsoid algorithm of Shor, Nemirovksy, and Yudin are guaranteed to minimize it. In this paper we describe relevant background material and a simple interior point method that solves such problems more efficiently. The algorithm is a variation on Huard's method of centers, using a selfconcordant barrier for matrix inequalities developed by Nesterov and Nemirovsky. (Nesterov and Nemirovsky have also extended their potential reduction methods to handle the same problem [NN91b].) Since the problem is quasiconvex but not convex, devising a nonheuristic stopping criterion (i.e., one that guarantees a given accuracy) is more difficult than in the convex case. We describe several nonheuristic stopping criteria that are based on the dual of a related convex problem and a new ellipsoidal approximation that is slightly sharper, in some cases, than a more general result due to Nesterov and Nemirovsky. The algorithm is demonstrated on an example: determining the quadratic Lyapunov function that optimizes a decay rate estimate for a differential inclusion.
Global Optimization in Control System Analysis and Design
 CONTROL AND DYNAMIC SYSTEMS: ADVANCES IN THEORY AND APPLICATIONS
, 1992
"... Many problems in control system analysis and design can be posed in a setting where a system with a fixed model structure and nominal parameter values is affected by parameter variations. An example is parametric robustness analysis, where the parameters might represent physical quantities that are ..."
Abstract

Cited by 11 (2 self)
 Add to MetaCart
Many problems in control system analysis and design can be posed in a setting where a system with a fixed model structure and nominal parameter values is affected by parameter variations. An example is parametric robustness analysis, where the parameters might represent physical quantities that are known only to within a certain accuracy, or vary depending on operating conditions etc. Frequently asked questions here deal with performance issues: "How bad can a certain performance measure of the system be over all possible values of the parameters?" Another example is parametric controller design, where the parameters represent degrees of freedom available to the control system designer. A typical question here would be: "What is the best choice of parameters, one that optimizes a certain design objective?" Many of the questions above may be directly restated as optimization problems: If q denotes the vector of parameters, Q
ECOLE POLYTECHNIQUE
"... A large time asymptotics for transparent potentials for the Manakov–Novikov–Veselov equation at positive energy ..."
Abstract
 Add to MetaCart
A large time asymptotics for transparent potentials for the Manakov–Novikov–Veselov equation at positive energy
Decentralized Information Processing in the Theory of Organizations
, 1997
"... Bounded rationality has been an important theme throughout the history of the theory of organizations, because it explains the sharing of information processing tasks and the existence of administrative sta s that coordinate large organizations. This article broadly surveys the theories of organizat ..."
Abstract
 Add to MetaCart
Bounded rationality has been an important theme throughout the history of the theory of organizations, because it explains the sharing of information processing tasks and the existence of administrative sta s that coordinate large organizations. This article broadly surveys the theories of organizations that model such bounded rationality and decentralized information processing. Author's address:
LIBOR ADDITIVE MODEL CALIBRATION TO SWAPTIONS MARKETS
, 2008
"... In the current paper, we introduce a new calibration methodology for the LIBOR market model driven by LIBOR additive processes based in an inverse problem. This problem can be splitted in the calibration of the continuous and discontinuous part, linking each part of the problem with atthemoney and ..."
Abstract
 Add to MetaCart
In the current paper, we introduce a new calibration methodology for the LIBOR market model driven by LIBOR additive processes based in an inverse problem. This problem can be splitted in the calibration of the continuous and discontinuous part, linking each part of the problem with atthemoney and in/outofthemoney swaption volatilies. The continuous part is based on a semidefinite programming (convex) problem, with constraints in terms of variability or robustness, and the calibration of the Lévy measure is proposed to calibrate inverting the Fourier Transform.