Theory primer

A four-page tour of the MPCC theory pympcc relies on. Skim it once if you’re new to MPCCs; it’s not a substitute for the references at the end of each page.

• Why MPCCs are hard
• Constraint qualifications
• Stationarity hierarchy
• Second-order sufficient conditions

Page	What it covers
Why MPCCs are hard	Standard form, why off-the-shelf NLP solvers fail, the reformulation idea.
Constraint qualifications	MPCC-LICQ, MPCC-MFCQ, why standard LICQ generically fails.
Stationarity hierarchy	S- / M- / C- / A- / W-stationarity and how to certify each.
Second-order sufficient conditions	Critical cone and reduced Hessian.