x = {1,…, 100}
f(x) = (x mod 6)2 mod 7 – sin(x)
x = 11
X = R
f(x) = -x4 + 1000×3 – 20×2 + 4x -6
optimization approaches
– generate & test: small input space, complex function
– calculus: function has derivative
– Newtons method
what if assumptions don’t hold?
big input space, complex function, no derivative (or hard to find)
possibly many local oftimg
Randomize optimization
Hill climbing
Guess xe x
repeat
let n = argmax f(n)
Un N(x)
if f(x) > f(x):x = n
else: stop
Thinking of a 5-bit sequence
f(x) = #correct bit
x: 5-bit sequences
