A MULTI-CLASS SUPPORT VECTOR MACHINE: THEORY AND MODEL

2013 ◽  
Vol 12 (06) ◽  
pp. 1175-1199 ◽  
Author(s):  
MINGHE SUN
Keyword(s):  
Support Vector Machine ◽  
Quadratic Programming ◽  
Programming Model ◽  
Inner Product ◽  
High Dimensional ◽  
Support Vector ◽  
Test Problems ◽  
Discriminant Functions ◽  
Input Space ◽  
Feature Spaces

A multi-class support vector machine (M-SVM) is developed, its dual is derived, its dual is mapped to high dimensional feature spaces using inner product kernels, and its performance is tested. The M-SVM is formulated as a quadratic programming model. Its dual, also a quadratic programming model, is very elegant and is easier to solve than the primal. The discriminant functions can be directly constructed from the dual solution. By using inner product kernels, the M-SVM can be built and nonlinear discriminant functions can be constructed in high dimensional feature spaces without carrying out the mappings from the input space to the feature spaces. The size of the dual, measured by the number of variables and constraints, is independent of the dimension of the input space and stays the same whether the M-SVM is built in the input space or in a feature space. Compared to other models published in the literature, this M-SVM is equally or more effective. An example is presented to demonstrate the dual formulation and solution in feature spaces. Very good results were obtained on benchmark test problems from the literature.

A new technique for generating quadratic programming test problems

1993 ◽  
Vol 61 (1-3) ◽  
pp. 215-231 ◽  
Author(s):  
Paul H. Calamai ◽  
Luis N. Vicente ◽  
Joaquim J. Júdice
Keyword(s):  
Quadratic Programming ◽  
New Technique ◽  
Test Problems ◽  
A New Technique

A Parallel Dual Projection Algorithm for Solving Positive Definite Quadratic Programming Problems

1990 ◽  
Author(s):  
Yugang Wang ◽  
Eric Sandgren
Keyword(s):  
Quadratic Programming ◽  
Positive Definite ◽  
Parallel Computer ◽  
Projection Algorithm ◽  
Test Problems ◽  
Local Optimum ◽  
Active Constraint ◽  
Search Point ◽  
Quadratic Programming Problems ◽  
Dual Projection

Abstract Two parallel algorithms, a dual projection algorithm and a hybrid dual projection algorithm, are proposed for solving positive definite quadratic programming problems. In each iteration of the algorithms, the search point is always a local optimum point on the current active constraint basis for both adding and dropping constraint operations. The advantage of this strategy is that the computation is stable and all operations maintain parallel properties. Only a pseudo-inverse matrix must be updated instead of two matrices in Goldfarb’s dual algorithm in a basis change. Both computational and space complexities are reduced by about half. When the search point reaches a vertex in the dual space, a pivot operation is employed to update the basis in the hybrid dual projection algorithm in place of the addition and deletion operations in the dual projection algorithm. This reduces the computational complexity by half in future iterations. Some suggestions are presented to further enhance the computational speed of the algorithm. Numerical results are presented based on randomly generated test problems. Comparison with other methods demonstrates that the new algorithm is efficient and stable and points to the possibility of implementation on a parallel computer.

scholarly journals Randomly Generated Test Problems for Positive Definite Quadratic Programming

1984 ◽  
Vol 10 (1) ◽  
pp. 86-96 ◽  
Author(s):  
Melanie L. Lenard ◽  
Michael Minkoff
Keyword(s):  
Quadratic Programming ◽  
Positive Definite ◽  
Test Problems

An Investigation of Pshenichnyi’s Recursive Quadratic Programming Method for Engineering Optimization

1987 ◽  
Vol 109 (2) ◽  
pp. 248-253 ◽  
Author(s):  
G. A. Gabriele ◽  
T. J. Beltracchi
Keyword(s):  
Quadratic Programming ◽  
Optimization Problems ◽  
Programming Algorithm ◽  
Test Problems ◽  
Engineering Optimization ◽  
Active Set ◽  
Original Algorithm ◽  
Recursive Quadratic Programming ◽  
Modified Algorithm ◽  
Engineering Optimization Problems

This paper discusses Pshenichnyi’s recursive quadratic programming algorithm for use in engineering optimization problems. An evaluation of the original algorithm is offered and several modifications are presented. The modifications include; addition of a variable metric update of the Hessian, an improved active set criterion, direct inclusion of the variable bounds, a divergence control mechanism, and updating schemes for the algorithm parameters. Implementations of the original algorithm and the modified algorithm were tested against the Sandgren test set of 23 engineering optimization problems. The results indicate that the modified algorithm was able to solve 20 of the 23 test problems while the original algorithm solved only 11. The modified algorithm was more efficient than the original on all the test problems.

Tire Modeling by Finite Elements

1992 ◽  
Vol 20 (1) ◽  
pp. 33-56 ◽  
Author(s):  
L. O. Faria ◽  
J. T. Oden ◽  
B. Yavari ◽  
W. W. Tworzydlo ◽  
J. M. Bass ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Rolling Contact ◽  
Test Problems ◽  
State Behavior ◽  
Normal Contact ◽  
New Developments ◽  
Applied Torque ◽  
Dimensional Finite Element ◽  
Tire Modeling ◽  
Three Dimensional Finite Element

Abstract Recent advances in the development of a general three-dimensional finite element methodology for modeling large deformation steady state behavior of tire structures is presented. The new developments outlined here include the extension of the material modeling capabilities to include viscoelastic materials and a generalization of the formulation of the rolling contact problem to include special nonlinear constraints. These constraints include normal contact load, applied torque, and constant pressure-volume. Several new test problems and examples of tire analysis are presented.

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