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 leave-one-out method and the VC-dimension are given. Experimental results on optical character recognition problems demonstrate the good generalization obtained when compared with other learning algorithms.

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A new primal-dual algorithm is proposed for the minimization of non-convex objective functions subject to simple bounds and linear equality constraints. The method alternates between a classical primal-dual step and a Newton-like step in order to ensure descent on a suitable merit function. Convergence of a well-defined subsequence of iterates is proved from arbitrary starting points. Algorithmic variants are discussed and preliminary numerical results presented. 1 IBM T.J. Watson Research Center, P.O.Box 218, Yorktown Heights, NY 10598, USA Email : arconn@watson.ibm.com 2 Department for Computation and Information, Rutherford Appleton Laboratory, Chilton, Oxfordshire, OX11 0QX, England, EU Email : nimg@letterbox.rl.ac.uk 3 Current reports available by anonymous ftp from joyous-gard.cc.rl.ac.uk (internet 130.246.9.91) in the directory "pub/reports". 4 Department of Mathematics, Facult'es Universitaires ND de la Paix, 61, rue de Bruxelles, B-5000 Namur, Belgium, EU Email : pht@ma...

We describe a framework for time-critical rendering of graphics scenes composed of a large number of objects having complex geometric descriptions. Our technique relies upon a scene description in which objects are represented as multiresolution meshes. We perform a constrained optimization at each frame to choose the resolution of each potentially visible object that generates the best quality image while meeting timing constraints. The technique provides smooth level-of-detail control and aims at guaranteeing a uniform, bounded frame rate even for widely changing viewing conditions. The optimization algorithm is independent from the particular data structure used to represent multiresolution meshes. The only requirements are the ability to represent a mesh with an arbitrary number of triangles and to traverse a mesh structure at an arbitrary resolution in a short predictable time. A data structure satisfying these criteria is described and experimental results are discussed. Keyword...

We deal with the primal-dual Newton method for linear optimization (LO). Nowadays, this method is the working horse in all efficient interior point algorithms for LO, and its analysis is the basic element in all polynomiality proofs of such algorithms. At present there is still a gap between the practical behavior of the algorithms and the theoretical performance results, in favor of the practical behavior. This is especially true for so-called large-update methods. We present some new analysis tools, based on a proximity measure introduced by Jansen et al., in 1994, that may help to close this gap. This proximity measure has not been used in the analysis of large-update method before. Our new analysis not only provides a unified way for the analysis of both large-update and small-update methods, but also improves the known iteration bounds. Keywords: Linear optimization, interior-point method, primal-dual method, proximity measure, polynomial complexity. AMS Subject Classification: 9...

In this paper, we first introduce the notion of self-regular functions. Various appealing properties of self-regular functions are explored and we also discuss the relation between selfregular functions and the well-known self-concordant functions. Then we use such functions to define self-regular proximity measure for path-following interior point methods for solving linear optimization (LO) problems. Any self-regular proximity measure naturally defines a primal-dual search direction. In this way a new class of primal-dual search directions for solving LO problems is obtained. Using the appealing properties of self-regular functions, we prove that these new large-update path-following methods for LO enjoy a polynomial, O n q+1 2q log n iteration bound, where q ≥ 1 is the so-called barrier degree of the self-regular ε proximity measure underlying the algorithm. When q increases, this � bound approaches the √n n best known complexity bound for interior point methods, namely O log. Our unified �√n ε n analysis provides also the O log best known iteration bound of small-update IPMs. ε At each iteration, we need only to solve one linear system. As a byproduct of our results, we remove some limitations of the algorithms presented in [24] and improve their complexity as well. An extension of these results to semidefinite optimization (SDO) is also discussed.

subject includes all optimization problems other than linear programming problems, it is not usually the case. Optimization problems involving discrete valued variables (i. e., those which are restricted to assume values from speci ed discrete sets, such as 0-1 variables) are not usually considered under nonlinear programming, they are called discrete, ormixed-discrete optimization problems and studied separately. There are good reasons for this. To solve discrete optimization problems we normally need very special techniques (typically of some enumerative type) di erent from those needed to tackle continous variable optimization problems. So, the term nonlinear program usually refers to an optimization problem in which the variables are continuous variables, and the problem is of the following general form: minimize (x) subject to hi(x) =0 � i =1to m gp(x)> 0 � p =1to t