A Ljusternik-Schnirelman minimax algorithm for finding equality constrained saddle points and its application for solving eigen problems: part I. Algorithm and global convergence
Sign Up to like & getrecommendations! Published in 2019 at "Advances in Computational Mathematics"
DOI: 10.1007/s10444-018-9616-6
Abstract: In Yao (J. Sci. Comput. 66, 19–40 2016), two Ljusternik-Schnirelman minimax algorithms for capturing multiple free saddle points are developed from well-known Ljusternik-Schnirelman critical point theory, numerical experiment is carried out and global convergence is… read more here.
Keywords: saddle points; global convergence; schnirelman minimax; ljusternik schnirelman ... See more keywords
On experimentally locating saddle-points on a potential energy surface from observed dynamics
Sign Up to like & getrecommendations! Published in 2019 at "Mechanical Systems and Signal Processing"
DOI: 10.1016/j.ymssp.2019.05.002
Abstract: Abstract This paper details a new method to estimate the location of unstable equilibria, specifically saddle-points, based on transient trajectories from experiments. We describe a system in which saddle-points (not easily observed in a direct… read more here.
Keywords: saddle points; energy surface; system; potential energy ... See more keywords
Small Alcohols Revisited: CCSD(T) Relative Potential Energies for the Minima, First- and Second-Order Saddle Points, and Torsion-Coupled Surfaces
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DOI: 10.1021/acsomega.7b01367
Abstract: The elucidation of conformations and relative potential energies (rPEs) of small molecules has a long history across a diverse range of fields. Periodically, it is helpful to revisit what conformations have been investigated and to… read more here.
Keywords: order saddle; minima first; saddle points; relative potential ... See more keywords
Semi-classical states for elliptic system near saddle points of potentials
Sign Up to like & getrecommendations! Published in 2023 at "Nonlinearity"
DOI: 10.1088/1361-6544/acd045
Abstract: In this paper, we study the following Hamiltonian elliptic system −ε2Δu+u=Hv(x,u,v) in RN,−ε2Δv+v=Hu(x,u,v) in RN,u(x)→0, v(x)→0 as |x|→∞, where ɛ > 0 is a small parameter, H is a super-quadratic sub-critical Hamiltonian. Our investigation focuses on the cases that H(x,u,v)=12K(x)(u2+v2)+F(u,v) and H(x,u,v)=K(x)F(u,v) , where… read more here.
Keywords: classical states; states elliptic; saddle points; elliptic system ... See more keywords
Escaping Saddle Points for Successive Convex Approximation
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Signal Processing"
DOI: 10.1109/tsp.2021.3138242
Abstract: Optimizing non-convex functions is of primary importance in modern pattern recognition because it underlies the training of deep networks and nonlinear dimensionality reduction. First-order algorithms under suitable randomized perturbations or step-size rules have been shown… read more here.
Keywords: convex approximation; order; successive convex; first order ... See more keywords
Criteria of saddle points for the general form of vector optimization problem in complex space
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DOI: 10.2298/fil2001221e
Abstract: In this paper, the criteria of the saddle point type for a general form of complex multi-objective programming problems are derived where the objective function of the problem is considered full complex. The criteria with/without… read more here.
Keywords: general form; saddle points; criteria saddle; problem ... See more keywords
Noise Helps Optimization Escape From Saddle Points in the Synaptic Plasticity
Sign Up to like & getrecommendations! Published in 2020 at "Frontiers in Neuroscience"
DOI: 10.3389/fnins.2020.00343
Abstract: Numerous experimental studies suggest that noise is inherent in the human brain. However, the functional importance of noise remains unknown. n particular, from a computational perspective, such stochasticity is potentially harmful to brain function. In… read more here.
Keywords: saddle points; noise; synaptic plasticity; escape saddle ... See more keywords
Entanglement Renyi Entropy of Two Disjoint Intervals for Large c Liouville Field Theory
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DOI: 10.3390/e24121758
Abstract: Entanglement entropy (EE) is a quantitative measure of the effective degrees of freedom and the correlation between the sub-systems of a physical system. Using the replica trick, we can obtain the EE by evaluating the… read more here.
Keywords: entanglement renyi; function; two disjoint; entropy ... See more keywords