dual variables handling in SDP solver(s)

[dimpase]

At present only primal variables are made available in SemidefiniteProgram(), although the dual variables are typically also provided by backends. This ticket added access to dual (and slack) variables.

Depends on #19072

CC: @sagetrac-srobik @mkoeppe @kiwifb

Component: numerical

Author: Dima Pasechnik

Branch: 572b630

Reviewer: Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/20506

[dimpase]

comment:1

the dependence on #19072 may be ignored for all practical purposes.

[mkoeppe]

comment:2

I'm a bit puzzled why you would want doctests for the particular floating point noise that you get from this version of the solver. Seems like extra work every time the package is upgraded?

[dimpase]

comment:3

Replying to @mkoeppe:

I'm a bit puzzled why you would want doctests for the particular floating point noise that you get from this version of the solver. Seems like extra work every time the package is upgraded?

I tried to round things using '...' etc as much as possible. I can in principle go
further with replacing things like

    sage: (p.slack(0)*p.dual_variable(0)).trace()
    1.71...e-07

by

    sage: 0.0e0 <= (p.slack(0)*p.dual_variable(0)).trace() < 1.75e-07
    True

Eventually we should think how to adapt your testing framework to SDP.

[mkoeppe]

comment:4

How about

sage: (p.slack(0)*p.dual_variable(0)).trace()  # tol 1e-6
0

[sagetrac-git]

Changed commit from 73e2bf6 to df80c5a

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

df80c5a

using #tol

[dimpase]

comment:6

Replying to @mkoeppe:

How about

sage: (p.slack(0)*p.dual_variable(0)).trace()  # tol 1e-6
0

good idea, fixed!

[mkoeppe]

comment:7

There are more places in the file that could use the #tol.
And perhaps there should be an example in which the slack is not 0.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

b91e62d

example with non-0 slack

[sagetrac-git]

Changed commit from df80c5a to b91e62d