Implement infinite bounds in Relay

[vacary]

The goal is treat explicitly infinite bounds in RelayProblem.

How to encode it ? How to avoid the duplication of variable ?

[radarsat1]

Towards this, a small test program would help and we can fix bugs from there.

[xhub]

I think a big part of the work it to rework and agree the data structure terminology. Relay is something quite specific that is part of the siconos lingo. What we would like to support is a box-constraint AVI, or MCP à la Ferris (not Pang).

I'm also unsure of what the goal is by " treat explicitly infinite bounds". Are we talking about just supporting arbitrary bounds in some solvers or implementing solvers that exploit the unboundedness? I understand it has the former. The latter would be detecting structure and identify which part of the problem correspond to equality constraints / complementarity.

Looking at the solvers, I would propose to have the following solvers:

• direct solvers: PATH, PATHAVI, PSOR, PGS, QiLSA (all of those can handle arbitrary bounds)
• reformulation to LCP, and QP

[vacary]

Fully agree with @xhub
The goal is to support arbitrary bounds.

[vacary]

Transfered to wish list in wiki

https://github.com/siconos/siconos/wiki/Wish-list-and-enhancement