A nonmonotone line search technique for Newton's method
SIAM Journal on Numerical Analysis
A training algorithm for optimal margin classifiers
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
The nature of statistical learning theory
The nature of statistical learning theory
Machine Learning
Continuous characterizations of the maximum clique problem
Mathematics of Operations Research
Making large-scale support vector machine learning practical
Advances in kernel methods
Fast training of support vector machines using sequential minimal optimization
Advances in kernel methods
Gradient Method with Retards and Generalizations
SIAM Journal on Numerical Analysis
Graph Partitioning and Continuous Quadratic Programming
SIAM Journal on Discrete Mathematics
Algorithm 813: SPG—Software for Convex-Constrained Optimization
ACM Transactions on Mathematical Software (TOMS)
The Barzilai and Borwein Gradient Method for the Large Scale Unconstrained Minimization Problem
SIAM Journal on Optimization
Nonmonotone Spectral Projected Gradient Methods on Convex Sets
SIAM Journal on Optimization
A Tutorial on Support Vector Machines for Pattern Recognition
Data Mining and Knowledge Discovery
Convergence of a Generalized SMO Algorithm for SVM Classifier Design
Machine Learning
Interior-Point Methods for Massive Support Vector Machines
SIAM Journal on Optimization
Relaxed Steepest Descent and Cauchy-Barzilai-Borwein Method
Computational Optimization and Applications
Large-Scale Active-Set Box-Constrained Optimization Method with Spectral Projected Gradients
Computational Optimization and Applications
SMO algorithm for least-squares SVM formulations
Neural Computation
Incorporating Invariances in Support Vector Learning Machines
ICANN 96 Proceedings of the 1996 International Conference on Artificial Neural Networks
Comparison of View-Based Object Recognition Algorithms Using Realistic 3D Models
ICANN 96 Proceedings of the 1996 International Conference on Artificial Neural Networks
Training Support Vector Machines: an Application to Face Detection
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Support Vector Machines: Training and Applications
Support Vector Machines: Training and Applications
Lagrangian support vector machines
The Journal of Machine Learning Research
Efficient svm training using low-rank kernel representations
The Journal of Machine Learning Research
Fast SVM Training Algorithm with Decomposition on Very Large Data Sets
IEEE Transactions on Pattern Analysis and Machine Intelligence
A New Conjugate Gradient Method with Guaranteed Descent and an Efficient Line Search
SIAM Journal on Optimization
Improvements to Platt's SMO Algorithm for SVM Classifier Design
Neural Computation
Training linear SVMs in linear time
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
New algorithms for singly linearly constrained quadratic programs subject to lower and upper bounds
Mathematical Programming: Series A and B
Fast Kernel Classifiers with Online and Active Learning
The Journal of Machine Learning Research
Working Set Selection Using Second Order Information for Training Support Vector Machines
The Journal of Machine Learning Research
A New Active Set Algorithm for Box Constrained Optimization
SIAM Journal on Optimization
QP Algorithms with Guaranteed Accuracy and Run Time for Support Vector Machines
The Journal of Machine Learning Research
Maximum-Gain Working Set Selection for SVMs
The Journal of Machine Learning Research
Parallel Software for Training Large Scale Support Vector Machines on Multiprocessor Systems
The Journal of Machine Learning Research
An Efficient Implementation of an Active Set Method for SVMs
The Journal of Machine Learning Research
LIBLINEAR: A Library for Large Linear Classification
The Journal of Machine Learning Research
An affine-scaling interior-point CBB method for box-constrained optimization
Mathematical Programming: Series A and B
Computational Optimization and Applications
Using an iterative linear solver in an interior-point method for generating support vector machines
Computational Optimization and Applications
LIBSVM: A library for support vector machines
ACM Transactions on Intelligent Systems and Technology (TIST)
Exploiting separability in large-scale linear support vector machine training
Computational Optimization and Applications
The analysis of decomposition methods for support vector machines
IEEE Transactions on Neural Networks
On the convergence of the decomposition method for support vector machines
IEEE Transactions on Neural Networks
Asymptotic convergence of an SMO algorithm without any assumptions
IEEE Transactions on Neural Networks
Margin maximization in spherical separation
Computational Optimization and Applications
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An affine-scaling algorithm (ASL) for optimization problems with a single linear equality constraint and box restrictions is developed. The algorithm has the property that each iterate lies in the relative interior of the feasible set. The search direction is obtained by approximating the Hessian of the objective function in Newton's method by a multiple of the identity matrix. The algorithm is particularly well suited for optimization problems where the Hessian of the objective function is a large, dense, and possibly ill-conditioned matrix. Global convergence to a stationary point is established for a nonmonotone line search. When the objective function is strongly convex, ASL converges R-linearly to the global optimum provided the constraint multiplier is unique and a nondegeneracy condition holds. A specific implementation of the algorithm is developed in which the Hessian approximation is given by the cyclic Barzilai-Borwein (CBB) formula. The algorithm is evaluated numerically using support vector machine test problems.