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We describe a family of descent algorithms which generalizes common existingschemes used in applications such as neural network training and more broadlyfor optimization of smooth functions--potentially for global optimization, oras a local optimization method to be deployed within global optimizationschemes like basin hopping. By introducing an auxiliary degree of freedom wecreate a dynamical system with improved stability, reducing oscillatory modesand accelerating convergence to minima. The resulting algorithms are simple toimplement and control, and convergence can be shown directly by Lyapunov'ssecond method.  Although this framework, which we refer to as friction-adaptive descent(FAD), is fairly general, we focus most of our attention here on a specificvariant: kinetic energy stabilization (which can be viewed as azero-temperature Nos\'e--Hoover scheme but with added dissipation in bothphysical and auxiliary variables), termed KFAD (kinetic FAD). To illustrate theflexibility of the FAD framework we consider several other methods. in certainasymptotic limits, these methods can be viewed as introducing cubic damping invarious forms; they can be more efficient than linearly dissipated Hamiltoniandynamics in common optimization settings.  We present details of the numerical methods and show convergence for both thecontinuous and discretized dynamics in the convex setting by constructingLyapunov functions. The methods are tested using a toy model (the Rosenbrockfunction). We also demonstrate the methods for structural optimization foratomic clusters in Lennard--Jones and Morse potentials. The experiments showthe relative efficiency and robustness of FAD in comparison to linearlydissipated Hamiltonian dynamics.

Friction-adaptive descent: a family of dynamics-based optimization methods