SVM оптимизайия

In this project you will implement different optimization methods for training Support Vector Machines (supervised learning) in order to solve a classification problem.

Q1 :

Write a program to find the solution of the SVM dual quadratic problem.

Apply any procedure for identifying the values of the hyperparameters C and γ. To find the solution of the SVM dual quadratic problem, you can use any routine that exploits the gradient of the objective function. Note that using specific method for Quadratic Programming problems would be preferable and it will lead to better optimization performances.

Q2:

Use the same kernel and hyperparameters of Question 1. Write a program which implements a decomposition method for the dual quadratic problem with any even value q ≥ 4. You must define the selection rule of the working set, construct the subproblem at each iteration and use a standard algorithm for its solution. You can use any routine that exploits the gradient of the objective function. However the use of specific method for quadratic programming would be preferable. You must implement in the outer optimization loop a stopping criterion based on the optimality conditions.

Q3:

Fix the dimension of the subproblem to q = 2 and implement the most violating pair (MVP) decomposition method which uses the analytic solution of the subproblems.