凸优化课业代写 Q1: (1) Given the data “Ranking Ivies’ Football Teams” and Massey’s least squares problem, respectively, on Slide 14 and 18 of Lecture 5:
(1) Given the data “Ranking Ivies’ Football Teams” and Massey’s least squares problem, respectively, on Slide 14 and 18 of Lecture 5:
https://www.cs.cityu.edu.hk/~cheewtan/CSCVXClass/LecRank.pdf, implement the gradient descent method with exact line search (see Slide 12 of the lecture slides): http://www.cs.cityu.edu.hk/~cheewtan/CSCVXClass/Lec5.pdf to answer which is the best team?
Validate your algorithm’s performance using the Theorem for the Gradient Descent Method stated on Slide 12. Then, implement the Newton’s Method and compare the performance of these two algorithms.
(1) Let’s examine some fundamental inequalities like what we saw during the GP Lecture and bring a machine to bear on them. You are encouraged to think originally and record your own findings along with any logical reasoning in your attempt. You can use any kind of algorithm for computation, e.g., gradient descent, Newton’s method, CVX interior-point solver etc, to compute your numerical solution.
(i) Can you use generalized GP to validate or prove the Nesbitt’s inequality on Slide 15 of the GP Lecture: https://www.cs.cityu.edu.hk/~cheewtan/CSCVXClass/Lec10.pdf?
(ii) Can you adapt your technique to prove or validate the Ky Fan inequality
Ky Fan (1914 – 2010) was a Chinese-born American mathematician (Professor of Mathematics at the University of California, Santa Barbara) who contributed to the foundation of semidefinite programming (that we explore later) in his seminal work with Richard Bellman.
(iii) What are some applications of the Nesbitt’s inequality or the Ky Fan’s inequality that you can think of?