- #1

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- Homework Statement
- You are at the point (0,1). Find the minimum of the function in the direction (line) (1, 2)^T using

the Golden-Section line-search algorithm on the step-length interval [0, 1]. Stop when the length of

the interval is less than 0.2. Note: step-length interval could be described by the parameter t, and,

so, all the points along the direction (1, 2)^T

can be expressed as (0, 1) + t · (1, 2).

- Relevant Equations
- Function is: f(x1,x2)=(x2-x1^2)^2+e^x1^2

Golden Ratio (GR):0.618

My function is f(x

I understand the equation for finding a point is x

_{1},x_{2})=(x_{2}-x_{1}^{2})^{2}+e^{x1}^^{2}I understand the equation for finding a point is x

_{k+1}=x_{k}+α_{k}d_{k}, where d_{k}=(0,1) and x_{0}=(0,1). For the first step I can choose α_{1}=0.618 (GR), but how do we choose α_{2}? In the solution manual I see they chose 0.382, was this just some arbitrary number? My assumption is that it is arbitrary. I understand afterwards I will have to compare f(x_{1}) and f(x_{2}). But I am struggling with how the second α_{2}was picked, any help would be appreciated.