generalization of iprox for L0 and L1 norm if D is not positive

[MohamedLaghdafHABIBOULLAH]

No description provided.

[MohamedLaghdafHABIBOULLAH]

@dpo Dans cette PR, je laisse la possibilité à D d'être négatif pour le calcul de iprox de l0 et l1, qu'en penses tu ?

[MohamedLaghdafHABIBOULLAH]

We can see that some tests pass (as they do locally on my PC); however, others, such as those on Julia nightly, are failing.
Any ideas, @dpo, on how we might avoid these failures?

[dpo]

Where and why do you need this generalization? How would $$d_i \leq 0$$ occur in practice? I presume it only concerns R2DH?

[MohamedLaghdafHABIBOULLAH]

Yes only for R2DH.

[dpo]

See my questions above.

Also, many tests fail.

[dpo]

@MohamedLaghdafHABIBOULLAH

[MohamedLaghdafHABIBOULLAH]

@dpo It might happen, especially with PSB and Andrei updates, which are not guaranteed to be positive.

For example in the case of PSB update:

julia> R2DH(DiagonalPSBModel(f), h, opt; x0 = x0, Mmonotone = 1)
[ Info:   iter     f(x)     h(x)  √(ξ/ν)        ρ       σ     ‖x‖     ‖s‖  
[ Info: ("norm of s ", 3.7705663200486095)
[ Info: ("norm of nabla f", 6.302436985231341)
[ Info: ("mks: ", -2.5481765450276903)
[ Info:      1  2.0e+01  0.0e+00 1.6e+00  2.6e+00 6.1e-06 0.0e+00 3.8e+00 ↘
[ Info: ("norm of s ", 11.100407554306303)
[ Info: ("norm of nabla f", 4.186821296105305)
[ Info: ("mks: ", -2.2413095031339463)
[ Info:      2  8.8e+00  4.6e+00 2.6e+00 -1.9e+00 2.0e-06 3.8e+00 1.1e+01 ↗
[ Info: ("norm of s ", 11.099398834542306)
[ Info: ("norm of nabla f", 4.186821296105305)
[ Info: ("mks: ", -2.2410608099582037)
[ Info:      3  8.8e+00  4.6e+00 2.6e+00 -1.9e+00 6.1e-06 3.8e+00 1.1e+01 ↗
[ Info: ("norm of s ", 11.096374140275897)
[ Info: ("norm of nabla f", 4.186821296105305)
[ Info: ("mks: ", -2.2403150015298623)
[ Info:      4  8.8e+00  4.6e+00 2.6e+00 -1.9e+00 1.8e-05 3.8e+00 1.1e+01 ↗
[ Info: ("norm of s ", 11.087313222194489)
[ Info: ("norm of nabla f", 4.186821296105305)
[ Info: ("mks: ", -2.238080012618819)
[ Info:      5  8.8e+00  4.6e+00 2.6e+00 -1.9e+00 5.4e-05 3.8e+00 1.1e+01 ↗
[ Info: ("norm of s ", 11.06024839920756)
[ Info: ("norm of nabla f", 4.186821296105305)
[ Info: ("mks: ", -2.231396878752057)
[ Info:      6  8.8e+00  4.6e+00 2.6e+00 -1.8e+00 1.6e-04 3.8e+00 1.1e+01 ↗
[ Info: ("norm of s ", 10.980100639234266)
[ Info: ("norm of nabla f", 4.186821296105305)
[ Info: ("mks: ", -2.2115414561597335)
[ Info:      7  8.8e+00  4.6e+00 2.6e+00 -1.8e+00 4.9e-04 3.8e+00 1.1e+01 ↗
[ Info: ("norm of s ", 10.74869789925592)
[ Info: ("norm of nabla f", 4.186821296105305)
[ Info: ("mks: ", -2.153655742439346)
[ Info:      8  8.8e+00  4.6e+00 2.6e+00 -1.7e+00 1.5e-03 3.8e+00 1.1e+01 ↗
[ Info: ("norm of s ", 10.126767542519968)
[ Info: ("norm of nabla f", 4.186821296105305)
[ Info: ("mks: ", -1.9935554978604637)
[ Info:      9  8.8e+00  4.6e+00 2.6e+00 -1.3e+00 4.4e-03 3.8e+00 1.0e+01 ↗
[ Info: ("norm of s ", 8.727820610764983)
[ Info: ("norm of nabla f", 4.186821296105305)
[ Info: ("mks: ", -1.6047462352009978)
[ Info:     10  8.8e+00  4.6e+00 2.5e+00 -6.8e-01 1.3e-02 3.8e+00 8.7e+00 ↗
[ Info: ("norm of s ", 6.572155195026285)
[ Info: ("norm of nabla f", 4.186821296105305)
[ Info: ("mks: ", -0.8568680860428097)
[ Info:     11  8.8e+00  4.6e+00 2.4e+00  2.6e-01 4.0e-02 3.8e+00 6.6e+00 =
[ Info: ("norm of s ", 3.9891122425220558)
[ Info: ("norm of nabla f", 3.796567352321169)
[ Info: ("mks: ", 1.1511857240755825)
[ Info:     12  7.2e+00  4.7e+00 1.9e+00  1.1e+00 4.0e-02 9.9e+00 4.0e+00 ↘
[ Info: ("norm of s ", 1.4205957290778362)
[ Info: ("norm of nabla f", 2.396822923688443)
[ Info: ("mks: ", 4.5811351144166945)
[ Info:     13  2.9e+00  5.0e+00 6.7e-01  1.7e+00 1.3e-02 8.3e+00 1.4e+00 ↘
[ Info: ("norm of s ", Inf)
[ Info: ("norm of nabla f", 1.9625297373911559)
[ Info: ("mks: ", NaN)

[MohamedLaghdafHABIBOULLAH]

I still though don’t really understand why the other tests are failing — all tests pass on my machine.