[Utilities] add distance_to_set for SecondOrderCone #2060
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we need to be very careful with distance to set with exponentials. We corrected it several times with @tjdiamandis because it is still ongoing research due to its numerical instability |
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A great reference for this is https://docs.mosek.com/whitepapers/expcone-proj.pdf (Section 5 and Lemma 5.1, specifically). |
We could just convert to |
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I added a test for an |
| # Parikh, N., & Boyd, S. (2014). Proximal algorithms. Foundations and | ||
| # trends in Optimization, page 184, section 6.3.2. | ||
| t, rhs = x[1], LinearAlgebra.norm(@views x[2:end]) | ||
| if rhs <= -t # Projection to the point (0, [0]) |
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No, I think I mean (0, [0])? I just followed Section 6.3.2 here: https://web.stanford.edu/~boyd/papers/pdf/prox_algs.pdf
| # trends in Optimization, page 184, section 6.3.2. | ||
| t, rhs = x[1], LinearAlgebra.norm(@views x[2:end]) | ||
| if rhs <= -t # Projection to the point (0, [0]) | ||
| return LinearAlgebra.norm(x) |
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Why don't we also do sqrt(2)/2 abs(t - rhs) ?
src/Utilities/distance_to_set.jl
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| t, rhs = x[1], LinearAlgebra.norm(@views x[2:end]) | ||
| if rhs <= -t # Projection to the point (0, [0]) | ||
| return LinearAlgebra.norm(x) | ||
| elseif t >= rhs # Projection to the point (t, x) |
odow
changed the title
Part of #2033.
We'll need to decide what sets we use exact methods for, and what we make up.
Boyd's book is: https://web.stanford.edu/~boyd/papers/pdf/prox_algs.pdf