A piecewise conservative method for unconstrained convex optimization

We consider a continuous-time optimization method based on dynamical system, where massive particle starting at rest moves in the conservative force field generated by objective function, without any kind of friction. formulate restart criterion mean dissipation kinetic energy, and we prove global convergence result for strongly-convex functions. Using Symplectic Euler discretization scheme, obtain an iterative algorithm. have considered discrete but also introduced new procedure ensuring each iteration decrease function greater than one achieved step classical gradient method. For algorithm, this last is capable guaranteeing result. apply same scheme to Nesterov Accelerated Gradient (NAG-C), use restarted NAG-C as benchmark numerical experiments. In smooth convex problems considered, our shows faster rate NAG-C. propose extension algorithm composite optimization: tests involving non-strongly functions with $\ell^1$-regularization, it has better performances well known efficient Fast Iterative Shrinkage-Thresholding Algorithm, accelerated adaptive scheme.