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Creators/Authors contains: "Ziyun Zhang"

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  1. (, Communications in mathematical sciences)
    WeproposetousetheL􏰀ojasiewiczinequalityasageneraltoolforanalyzingthecon- vergence rate of gradient descent on a Hilbert manifold, without resorting to the continuous gradient flow. Using this tool, we show that a Sobolev gradient descent method with adaptive inner product converges exponentially fast to the ground state for the Gross-Pitaevskii eigenproblem. This method can be extended to a class of general high-degree optimizations or nonlinear eigenproblems under cer- tain conditions. We demonstrate this generalization using several examples, in particular a nonlinear Schr ̈odinger eigenproblem with an extra high-order interaction term. Numerical experiments are pre- sented for these problems. 
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