The nature of statistical learning theory
The nature of statistical learning theory
On piecewise quadratic Newton and trust region problems
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
Fast training of support vector machines using sequential minimal optimization
Advances in kernel methods
SSVM: A Smooth Support Vector Machine for Classification
Computational Optimization and Applications
Lagrangian support vector machines
The Journal of Machine Learning Research
Improvements to Platt's SMO Algorithm for SVM Classifier Design
Neural Computation
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The Support vector machines can be posed as quadratic program problems in a variety of ways.This paper investigates a formulation using the two-norm for the misclassification error and appending a bias norm to objective function that leads to a positive definite quadratic program only with the nonnegative constraint under a duality construction. An unconstrained convex program problem, which minimizes a differentiable convex piecewise quadratic function, is proposed as the Lagrangian dual of the quadratic program. Then an exact semismooth Newton support vector machine (ESNSVM) is obtained to solve the program speedily. Some numerical experiments demonstrate that our algorithm is very efficient comparing with the similar algorithms such as LSVM.