lecture13

lecture13 - Advanced Computer Graphics Optimization Part 2...

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Advanced Computer Graphics Optimization Part 2 Professor Brogan
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Simulated Annealing Review of Metropolis Procedure Evaluation function Current state Temperature (and annealing schedule) Change in state
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Computing New States Lacking derivatives (and when data isn’t smooth) Doesn’t matter With derivatives If you know which way is downhill (better) Then why risk losing that improvement by picking a new direction randomly
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Going Downhill If you always use derivative to go downhill Metropolis step is ineffective (you’re always going to take the better answer) Process turns into a simple gradient descent algorithm
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Gradient Descent Follow derivatives downhill Performs poorly in narrow valleys And performs worse as the solution is reached
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Best of Both Worlds Current state = Simplex of N+1 points Not just one point Envision simplex with lines connecting N+1 points In three dimensions it is a tetrahedron The goal is for minimum to be spanned by points At each iteration, replace one point with a lower-valued one
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Simplex Method Diameter of simplex gets smaller with each iteration Stop when diameter reaches tolerance
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This note was uploaded on 01/23/2012 for the course CS 551 taught by Professor Staff during the Fall '10 term at Syracuse.

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lecture13 - Advanced Computer Graphics Optimization Part 2...

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