# Line Search Algorithm Assignment Help

## Line search algorithms

1. Uniform search
2. Dichotomous search
3. Golden section search

### 1. Uniform Search

Pick the search points α12,.....,αn so that they are uniformly spaced over some preset range α

• α* = argminα∈α12,.....,αn ƒ(α)
• + No assumptions about convexity or shape of ƒ(α)
• + Finds (nearly) a global minimum
• - Relatively inefficient

### 2. Dichotomous search

Suppose you know that α is in the range of αmin to αmax

• calculate the following evaluation points
• Otherwise, set αmin = b
• Repeat until convergence
• If the derivative dƒ(α)⁄dα can be calculated, the computation can be reduced to one evaluation of the derivative per an iteration.
• If the derivative is used, this is called bisection method.

### 3. Golden section line search

Suppose you know that α is in range of αmin to αmax

Loop to 2 until convergence

### 4. Quadratic fit line search

• Find α1, α2 and α3 such that ƒ(α1) ≥ ƒ(α2) and ƒ(α2) ≤ ƒ(α3)
• Find α* as the minimum to the quadratic fit of ƒ(α1), ƒ(α2), and ƒ(α3)
• If α α2,
if ƒ(α*) ƒ (α2), then αnew = α1, α2, α*
if ƒ(α*) ≤ ƒ (α2), then αnew = α2, α*, α3

Else

if ƒ(α*) ƒ (α2), then αnew = α*, α2, α3
if ƒ(α*) ≤ ƒ(α2), then αnew = α1, α*, α2
• Loop to 2 until convergence
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