Fast algorithms are proposed for the electronic structure
excited-state calculation in the configuration interaction framework. All
of them are based or inspired by an unconstrained nonconvex optimization
problem, which is a reformulation of the eigenvalue problem. Global
convergence to excited states instead of their invariant subspace is
guaranteed almost surely. Locally, algorithms converge linearly with
convergence rate depending on energy gaps. Momentum acceleration, exact
linesearch, and column locking are incorporated to further accelerate
algorithms and reduce computational costs. We demonstrate the efficiency
of these algorithms on a few FCI matrices.
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