An Affine-Scaling Interior-Point Method for Continuous Knapsack Constraints with Application to Support Vector Machines

2011 ◽  
Vol 21 (1) ◽  
pp. 361-390 ◽  
Author(s):  
Maria D. Gonzalez-Lima ◽  
William W. Hager ◽  
Hongchao Zhang
Keyword(s):  
Support Vector Machines ◽  
Interior Point ◽  
Interior Point Method ◽  
Point Method ◽  
Support Vector ◽  
Affine Scaling ◽  
Knapsack Constraints ◽  
Vector Machines

Exterior-Point Method for Support Vector Machines

2014 ◽  
Vol 25 (7) ◽  
pp. 1390-1393 ◽  
Author(s):  
Veronica Bloom ◽  
Igor Griva ◽  
Byong Kwon ◽  
Anna-Rose Wolff
Keyword(s):  
Support Vector Machines ◽  
Point Method ◽  
Support Vector ◽  
Vector Machines

scholarly journals FAST SOLVER FOR INTERIOR POINT METHOD OF SVM TRAINING BY PARALLEL GMRES AND HSS

2014 ◽  
pp. 116-124
Author(s):  
Di Zhao
Keyword(s):  
Quadratic Programming ◽  
Saddle Point ◽  
Interior Point ◽  
Interior Point Method ◽  
Saddle Point Problem ◽  
Point Method ◽  
Cholesky Factorization ◽  
Support Vector ◽  
Point Problem ◽  
Fast Solver

Support Vector Machine (SVM) is one of the latest statistical models for machine learning. The key problem of SVM training is an optimization problem (mainly Quadratic Programming). Interior Point Method (IPM) is one of mainstream methods to solve Quadratic Programming problem. However, when large-scale dataset is used in IPM based SVM training, computational difficulty happens because of computationally expensive matrix operations. Preconditioner, such as Cholesky factorization (CF), incomplete Cholesky factorization and Kronecker factorization, is an effective approach to decrease time complexity of IPM based SVM training. In this paper, we reformulate SVM training into the saddle point problem. As the research question that motivates this paper, based on parallel GMRES and recently developed preconditioner Hermitian/Skew-Hermitian Separation (HSS), we develop a fast solver HSS-pGMRES-IPM for the saddle point problem from SVM training. Computational results show that, the fast solver HSS-pGMRES-IPM significantly increases the solution speed for the saddle point problem from SVM training than the conventional solver CF.

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