scholarly journals Computable representation of the cone of nonnegative quadratic forms over a general second-order cone and its application to completely positive programming

2013 ◽  
Vol 9 (3) ◽  
pp. 701-719 ◽  
Author(s):  
Ye Tian ◽  
Shu-Cherng Fang ◽  
Zhibin Deng ◽  
Wenxun Xing
Keyword(s):  
Quadratic Forms ◽  
Second Order ◽  
Completely Positive ◽  
Second Order Cone ◽  
Computable Representation ◽  
Completely Positive Programming

scholarly journals A New Conic Approach to Semisupervised Support Vector Machines

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Ye Tian ◽  
Jian Luo ◽  
Xin Yan
Keyword(s):  
Quadratic Forms ◽  
Optimal Solution ◽  
Positive Cone ◽  
Support Vector ◽  
Completely Positive ◽  
Adaptive Scheme ◽  
Completely Positive Cone ◽  
Vector Machines ◽  
Programming Techniques ◽  
Completely Positive Programming

We propose a completely positive programming reformulation of the 2-norm soft marginS3VMmodel. Then, we construct a sequence of computable cones of nonnegative quadratic forms over a union of second-order cones to approximate the underlying completely positive cone. Anϵ-optimal solution can be found in finite iterations using semidefinite programming techniques by our method. Moreover, in order to obtain a good lower bound efficiently, an adaptive scheme is adopted in our approximation algorithm. The numerical results show that the proposed algorithm can achieve more accurate classifications than other well-known conic relaxations of semisupervised support vector machine models in the literature.

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