Ground-state characterization of constrained nonlinear eigenvalue minimizers

Establish whether the minimizers of the constrained local and second-level energy problems in the EMDD method correspond to the ground-state, or lowest-eigenvalue, solutions of the associated nonlinear eigenvalue problems without imposing additional assumptions.

Background

For nonlinear eigenvalue problems, the EMDD method solves constrained minimization problems on finite-dimensional intersections of the unit sphere with enriched local or coarse spaces. Although these problems admit minimizers, the paper notes that it is unresolved whether such minimizers necessarily represent ground states of the corresponding nonlinear eigenvalue problems. This issue matters because the global model problem is intended to compute the lowest-energy eigenstate, while finite-dimensional constrained subproblems may possess minimizers associated with other stationary states unless further structural assumptions are available.