Outline

1. OP1 : The original QP problem
2. Derivation of the decomposition matrix
3. OP2 : The transformed QP problem
4. Parallel Decomposition Technique (PDT) algorithm
5. Parallel Gradient Projection Method (PGPM) for STEP A2 of algorithm PDT
6. Parallel Gradient Updating (PGU) for STEP A3 of algorithm PDT

Define variables

• n = number of training data
• m = number of  features
•  

Training Support Vector Machines (SVM) for binary classification requires to solve the convex quadratic (QP) problem. 

QP problem(QP1)

subject to 

where

The derivation of the decomposition matrix

QP problem(QP2)

PDT Algorithm(1/2)

PDT Algorithm(2/2)

PGPM Algorithm(1/2)

PGPM Algorithm(2/2)

PGU Algorithm(1/2)

PGU Algorithm(2/2)