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