Week 3

Question 1

How does the Nelder-Mead method work? What are the steps?

Answer 1

1. Begin with simplex (x⁽⁰⁾, …, x^(d))
2. Do for g = 1, 2, …, K
   
   1. Sort x⁽⁰⁾, …, x^(d) s.t. f(x⁽⁰⁾) ≥ f(x⁽¹⁾) ≥ … ≥ f(x^(d)), with x⁽⁰⁾ is the worst point.
   2. Determine the average a^(bar), excluding the worst
   3. Update x⁽⁰⁾ with a better point, which lies in the line starting from x⁽⁰⁾ toward x^(bar), if no points found shrink the simplex by moving other points closer to the best point.

Question 2

How does the differrential evulolution method work?

Answer 2

1. Begin with generation g = 0, with population N points x^{(i, 0)}