Constrained High-Index Saddle Dynamics for the Solution Landscape with Equality Constraints

We propose a constrained high-index saddle dynamics (CHiSD) method to search for index-k points of an energy functional subject equality constraints. With Riemannian manifold tools, the CHiSD is derived in minimax framework, and its linear stability at point proved. To ensure property, numerically implemented using retractions vector transport. Then we present numerical approach by combining with downward upward algorithms construct solution landscape presence apply Thomson problem Bose–Einstein condensation as examples demonstrate efficiency proposed method.