Computational methods in optimization David F. Gleich Purdue - - PowerPoint PPT Presentation

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Dec 03, 2023 600 likes •829 views

Computational methods in optimization David F. Gleich Purdue University Thanks to Nick Henderson for many slides. 1 Course objectives To understand optimization To be able to optimize a function Course outline Background Software Least

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Computational methods in

ptimization

David F. Gleich Purdue University

1 Thanks to Nick Henderson for many slides.

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To understand optimization To be able to optimize a function

Course objectives

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Course outline

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Background

Software Least Squares Matrix calculus

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Unconstrained Optimization

Non-linear equations Newton methods Line search Trust region Quasi-newton

minimize ƒ()

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Constrained Optimization

Linear programming Quadratic programming Large-scale

minimize ƒ() subject to ≤

  

c()

   ≤

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Modern Topics

Convex Integer Stochastic

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Questions about topics?

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Your first quiz

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Source: http://xkcd.com/135/

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Raptors move at 25 m/s You move at 6 m/s

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But who cares?

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The new model

to minimize “likelihood” of being eaten subject to raptor motion human motion choose direction to run vp[j] for j = {1, . . . , N}

j=1 3

i=1

1 kp[j] ri[j]k2 dt ri[j + 1] = ri[j] + hvi p[j] ri[j] kp[j] ri[j]k p[j + 1] = p[j] + hvp[j]

Thanks to Nick Henderson for many slides.

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How it’s done

model modeling environment (AMPL) solver (SNOPT) web service (NEOS) direct (Matlab, C, Fortran)

Thanks to Nick Henderson for many slides.

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Solve!

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time = 2.65 sec

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Source: http://en.wikipedia.org/wiki/Velociraptor

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