Function resolve_solver 

pub fn resolve_solver(
    class: ProblemClass,
    selection: SolverSelection,
) -> Result<SolverChoice, String>

Resolve a ProblemClass and a SolverSelection into the solver to dispatch to, or an error string when a forced selection does not match the detected class.

auto routes LP / convex QP to the convex IPM (QpIpm) and convex QCQP to the conic IPM (SocpIpm); nonconvex QP and general NLP resolve to Nlp. A forced selection that does not match the detected class is rejected with a clear message.

QpActiveSet is the one forced selection that is not restricted to the convex classes: pounce-qp handles an indefinite Hessian by construction (§4.5 inertia control), which is what docs/src/choosing-a-solver.md has always advertised, so a NonconvexQp is accepted here and dispatched to it (gh #786). auto still sends that class to the NLP filter-IPM — the class is our inference, and the general path is the safer default for it — so this is reachable only by asking for the engine by name.

What the verdict on an indefinite QP does and does not mean (gh #848). This comment used to say the engine returns “a local solution”, reading §4.5 inertia control as a second-order guarantee. It is not one: inertia control shifts the KKT diagonal so each factorization has the right inertia, which makes the linear algebra work and says nothing about the curvature of P on the feasible directions at the point finally returned. On P = [[1, 5], [5, 1]] over [-1, 1]² the engine reported Optimal at the strict saddle x = 0, f = 0, where x = (1, -1) is feasible at f = -4.

Second-order evidence is now part of the verdict, from two guards that cover different classes (both described on pounce_convex::solve_qp_active_set_inertia). The engine certifies the reduced Hessian on its working set’s null space and, where it finds a witness of negative curvature, escapes along it and returns the better point — so the fix is usually a better answer rather than a worse status. The driver then screens what comes back by exhibition, which reaches the degenerate-active-bound class the first cannot, and refuses a verdict only where it holds a strictly better feasible point in hand.

Local, still, and not even that in general: seeing past every working set is the NP-hard part of nonconvex QP. sqp_qp_certify_second_order turns the engine-side check off.