A second-order gradient-like dissipative dynamical system with Hessian-driven damping.: Application to optimization and mechanics

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APPLICATIONS OF THE ŁOJASIEWICZ–SIMON, GRADIENT INEQUALITY TO GRADIENT-LIKE EVOLUTION EQUATIONS (2009, background): “For other types of second order ordinary differential equations to which the Lojasiewicz technique applies, see [1], [2].”
ASYMPTOTIC BEHAVIOR OF SECOND-ORDER DISSIPATIVE EVOLUTION EQUATIONS COMBINING POTENTIAL WITH NON-POTENTIAL EFFECTS ∗ (2009, background): “Geometrical damping is of great importance for numerical optimization, and modeling of non elastic shocks in mechanics, see [7].”
On the second-order asymptotical regularization of linear ill-posed inverse problems (2018, unknown): “an optimization viewpoint, establishing diﬀerent convergence results and identifying the circumstances under which the rate of convergence of HBF is better than the one of the ﬁrst order methods; see [1, 2, 3]. Numerical algorithms based on (1.4) for solving some special problems, e.g. inverse sourc”
Fast optimization via inertial dynamics with closed-loop damping (2020, background): “The introduction of the Hessian-driven damping allows to damp the transversal oscillations that might arise with (HBF), as observed in [9] in the case of the Rosenbrock function.”