## Search

Now showing items 11-17 of 17

#### 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 ...

#### Privacy-Preserving Horizontally Partitioned Linear Programs

(2010)

We propose a simple privacy-preserving reformulation of a linear program whose equality constraint
matrix is partitioned into groups of rows. Each group of matrix rows and its corresponding right hand side
vector are ...

#### 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 ...

#### Knowledge-Based Nonlinear Kernel Classi ers

(2003)

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

#### Equivalence of Minimal L0 and Lp Norm Solutions of Linear Equalities, Inequalities and Linear Programs for Sufficiently Small p

(2011)

For a bounded system of linear equalities and inequalities we show that the NP-hard ?0 norm minimization problem min
||x||0 subject to Ax = a, Bx ? b and ||x||? ? 1, is completely equivalent to the concave
minimization ...

#### Absolute Value Equation Solution via Dual Complementarity

(2011)

By utilizing a dual complementarity condition, we propose an iterative method for solving the NPhard
absolute value equation (AVE): Ax?|x| = b, where A is an n�n square matrix. The algorithm
makes no assumptions on the ...