Convex Optimization selections from Chapter 6xhx/courses/ConvexOpt/projects/... · 2011. 3. 7. ·...
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Convex Optimization selections from Chapter 6 Audrey Hesse
Transcript of Convex Optimization selections from Chapter 6xhx/courses/ConvexOpt/projects/... · 2011. 3. 7. ·...
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Convex Optimizationselections from Chapter 6
Audrey Hesse
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Approximation & Fitting
• Norm Approximation
– Penalty functions
• Least-norm problems
• Regularized Approximation
• Signal Reconstruction
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Norm Approximation
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• A solution to norm approximation is sometimes an approximate solution
Ax ≈ b
• Residual: vector r = Ax – b
• Residuals: the individual components of the residual associated with x
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Minimize: |}||,...,{|max|||| 1 mrrbAx
Minimize the sum of the squares of the residuals 22
2
2
1
2
2 ...|||| mrrrbAx
||...|||||||| 211 mrrrbAx Minimize:
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Implicit constraint +1
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)(
:subject to
||||minimize
2
2
2
bAxxf
bAx
x
T
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4000Rx
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Optimal trade-off curve
Knee at
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