## Search

Now showing items 1-10 of 11

#### Exactness Conditions for a Convex Differentiable Exterior Penalty for Linear Programming

(2007)

Sufficient conditions are given for a classical dual exterior penalty
function of a linear program to be independent of its penalty parameter.
This ensures that an exact solution to the primal linear program can be
obtained ...

#### A Newton Method for Linear Programming

(2002)

A fast Newton method is proposed for solving linear programs with
a very large ( 106) number of constraints and a moderate ( 102)
number of variables. Such linear programs occur in data mining and
machine learning. ...

#### Nonlinear Knowledge-Based Classification

(2006)

Prior knowledge over general nonlinear sets is incorporated into nonlinear kernel classification
problems as linear constraints in a linear program. The key tool in this incorporation is a theorem
of the alternative for ...

#### Knowledge-Based Linear Programming

(2003)

We introduce a class of linear programs with constraints in the form
of implications. Such linear programs arise in support vector machine
classi cation, where in addition to explicit datasets to be classi ed, prior
knowledge ...

#### Chunking for Massive Nonlinear Kernel Classification

(2006)

A chunking procedure [2] utilized in [18] for linear classifiers is proposed here for nonlinear kernel
classification of massive datasets. A highly accurate algorithm based on nonlinear support vector
machines that ...

#### Support Vector Machine Classi cation via Parameterless Robust Linear Programming

(2003)

We show that the problem of minimizing the sum of arbitrary-norm
real distances to misclassi ed points, from a pair of parallel bounding
planes of a classi cation problem, divided by the margin (distance) be-
tween the ...

#### Knowledge-Based Support Vector Machine Classi ers

(2001)

Prior knowledge in the form of multiple polyhedral sets, each belonging
to one of two categories, is introduced into a reformulation
of a linear support vector machine classi er. The resulting formulation
leads to a ...

#### Probability of Unique Integer Solution to a System of Linear Equations

(2009)

We consider a system of m linear equations in n variables Ax = d and give necessary and sufficient
conditions for the existence of a unique solution to the system that is integer: x ? {?1,1}n. We achieve this by
reformulating ...

#### Set Containment Characterization

(2001)

Characterization of the containment of a polyhedral set in a closed halfspace, a key factor in
generating knowledge-based support vector machine classi ers [7], is extended to the following:
(i) Containment of one ...

#### Data Selection for Support Vector Machine Classifiers

(2000)

The problem of extracting a minimal number of data points
from a large dataset, in order to generate a support vector
machine (SVM) classi er, is formulated as a concave minimization
problem and solved by a nite number ...