Analyzer for Initial Point

- NLP/Conic might converge poorly on bad points
- MIP/LP will discard an infeasible initial point (?)

We might be able to re-use the machinery of the Feasibility Analyzer

Start by reading the existing Feasibility Analyzer machinery mentioned in the issue and trace how it handles initial points. Clarify the expected behavior for NLP/Conic versus MIP/LP models, then define tests showing when an initial point is poorly converged or discarded; the work is complete when the analyzer reports these cases consistently.

Do mô hình lập chỉ mục viết ra từ nội dung của issue.