Trick to reduce problem size when both lower and upper inequality constraints are required

[EmanueleSiego]

Actually piqp manages inequality constraints of the form $Gx \leq h$.
If real problem requires both lower and upper constraints, say $k \leq \tilde{G}x \leq h$, then $G$ matrix used in the standard formulation doubles, $G = [\tilde{G} ; -\tilde{G}]$, and KKT matrix becomes larger.
Following the trick described in Marcel Jacobse, Christof Buskens - REVISITING DESIGN ASPECTS OF A QP SOLVER FOR WORHP, $\tilde{G}$ matrix can be directly used and better performances could be reached (at least in terms of time spent factoring the KKT matrix).

Do you think this is a possible improvement?

[RSchwan]

Thanks for the resource, very interesting read. I think, what they describe in the paper should be possible to implement, but requires a bit of remodeling of the solvers internals. I'm currently working on other optimizations (special KKT solver for OCP type structures with auto-detection, and warm-starting). But afterward, I will revisit this issue and see what I can do. This could be indeed very interesting in the context of SQP as described in the WHORP paper. It would also make the API more similar to IPOPT.

For now, I keep the issue open for future reference :)