[SCIP] Lack of initial estimation cuts by SOC constraint handler

[Stefan Vigerske]

Hi,

there is no good reason. It's just one of the loose ends that hasn't 
been tied up so far 
(https://github.com/scipopt/scip/blob/master/src/scip/nlhdlr_soc.c#L2513).

You could try adding some initial cuts as linear constraints.
1. Think of the constraint as sqrt(4 z^2 + (x-y)^2) <= x+y
2. Take the gradient on the left side. This should be
    1/f(x,y,z) (x,-y,4z), with f(x,y,z) = sqrt(4 z^2 + (x-y)^2)
3. For a point (x*,y*,z*), a valid cut is
    f(x*,y*,z*) + f'(x*,y*,z*) (x-x*, y-y*, z-z*) <= x+y,
    that is (please check),
    f(x*,y*,z*) + 1/f(x*,y*,z*) (x*(x-x*), -y*(y-y*), 4z*(z-z*)) <= x+y
4. Add these inequalities for a few choices of (x*,y*,z*), e.g.,
    (1,0,1), (0,1,1), (1,0,-1), (0,1,-1).

I agree that it would be nicer if SCIP were doing that automatically.

Stefan


On 7/15/22 18:13, liding xu wrote:
> Dear SCIP community,
>     I am solving a maximization MINLP problem with: a concave signomial
> objective function (geometric mean, \prod_{i in [n]} w_i^{1/n}), SOC
> constraints (z^2<=xy, x,y >=0), linear constraints. SCIP seems to have a
> numerical problem. The root node run outputs "(node 1) unresolved numerical
> troubles in LP 3 -- using pseudo solution instead (loop 1)".
> 
>    I try to enable debugging output of two constraint handlers:
> nlhdlr_convex.c and nlhdlr_soc.c. Both successfully detect the
> SOC/signomial structure. However, soc handler does not generate any
> estimation/initial cuts,  thus making the LP relaxation numerically ill. Do
> you know the reason why cuts for soc are not generated? The problem's gms
> file is attached.
>    Thank you.
> 
> Best regards,
> Liding Xu
> 
> 
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