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Accelerated Nehari manifold optimization methods for computing ground state solutions of coupled elliptic systems
Zhaoxing Chen, Wei Liu, Ziqing Xie +1
This paper presents a class of efficient algorithms for computing the ground state solutions of a semilinear elliptic system, which are unstable saddle points of the variational fu…
BDF schemes for accelerated gradient flows in projection-free approximation of nonconvex constrained variational minimization
Guozhi Dong, Zikang Gong, Ziqing Xie +1
We propose novel algorithms combining accelerated gradient flows with linearized projection-free treatments of non-convex constraints and BDF pseudo-temporal discretization for qua…
Nehari manifold optimization and its application for finding unstable solutions of semilinear elliptic PDEs
Zhaoxing Chen, Wei Liu, Ziqing Xie +1
A Nehari manifold optimization method (NMOM) is introduced for finding 1-saddles, i.e., saddle points with the Morse index equal to one, of a generic nonlinear functional in Hilber…
Second-order flows for approaching stationary points of a class of non-convex energies via convex-splitting schemes
Haifan Chen, Guozhi Dong, José A. Iglesias +2
This paper contributes to the exploration of a recently introduced computational paradigm known as second-order flows, which are characterized by novel dissipative hyperbolic parti…