Computational Optimization

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Computational Optimization

• Lab6 Active Set Methods 3/05

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Sign up for Talks

• Talks scheduled
• April 20 Jim
• Evaluations
• April 23 Phaedra,Fu
• April 27 Andrew/Sharath, Xiaoli, Zheng, Xingqun
  Projects due

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Laboratory 6

• Download .m files from course webpage
• Check out dnewtonlip.m
• This is a discrete newton method that
  calculates the Hessian via finite approximation.
  
• Linesearch is done by quadratic interpolation.
  
• Find the parts of the m files that compute the
  search direction and do the linesearch.
• Find the parts that do the active search.

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Exercise

• Try the method on the following problem
• with x0 8 2 and tol 1e-8, A 1 1 2
  -3.
• b3 6
• xmin,lambdamin,fxmin
• dnewtonlip('f','g',A,b,x0,tol)

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Examine output

• Make a diary of the run.
• Sketch the run.
• At each iteration,
• sketch x, indicate which constraints are
  active, provide the Lagrangian Multipliers.
  Note, you can use the Matlab debugger to examine
  any values of interest during the run.
• Check the optimality of the final solution.

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Uses QR factorization
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Computing Lagrangian Multipliers
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QR Efficiency

• QR factorization is especially nice
• Because the factorization can be update as
  columns of A or Rows of A are added and deleted.
• See qrinsert, qrdelete, qr in Matlab

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Exercise 2

• Repeat the previous exercise on the following
  problem
• with x0 0,0 and tol 1e-8

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Exercise 3

• Repeat the previous exercise on the following
  problem
• with x0 2 2 1 0 and tol 1e-8
• You will need to convert each inequality to two
  inequalities to use the software.

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Examine output

• Make a diary of the run.
• Sketch the run.
• At each iteration,
• sketch x, indicate which constraints are
  active, provide the Lagrangian Multipliers.
• Check the optimality of the final solution.