טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentPemov Ella
SubjectThe 2-Coordinate Descent Method for Solving Simplex-Type
Constrained Problems with Application to SVM
Training
DepartmentDepartment of Industrial Engineering and Management
Supervisor Professor Amir Beck
Full Thesis textFull thesis text - English Version


Abstract

In this work, we interested to find the solution of the problem of finding the minimum of f(x), a convex function constrained by aTx=b, x0.  Two well known problems that have the above form are Support Vector machine (SVM) in the linearly separable case and the Chebyshev center problem.

We propose a two coordinate descent method, where in each iteration, at the beginning, we choose one coordinate and the second coordinate is chosen with respect to the first chosen coordinate. We show the convergence rate of the proposed method. Several numerical experiments were made in order to compare the suggested method to the existing block coordinate methods.  The numerical experiments show that in most of the cases, the suggested method improved the results of the existing methods.