@article {2022,
	title = {A Gradient Flow Equation for Optimal Control Problems With End-point Cost},
	year = {2022},
	month = {2022/07/07},
	abstract = {In this paper, we consider a control system of the form $\dot x = F(x)u$, linear in the control variable u. Given a fixed starting point, we study a finite-horizon optimal control problem, where we want to minimize a weighted sum of an end-point cost and the squared 2-norm of the control. This functional induces a gradient flow on the Hilbert space of admissible controls, and we prove a convergence result by means of the Lojasiewicz-Simon inequality. Finally, we show that, if we let the weight of the end-point cost tend to infinity, the resulting family of functionals is Γ-convergent, and it turns out that the limiting problem consists in joining the starting point and a minimizer of the end-point cost with a horizontal length-minimizer path.},
	isbn = {1573-8698},
	url = {https://doi.org/10.1007/s10883-022-09604-2},
	author = {Alessandro Scagliotti}
}
@article {2022,
	title = {A piecewise conservative method for unconstrained convex optimization},
	volume = {81},
	year = {2022},
	month = {2022/01/01},
	pages = {251 - 288},
	abstract = {We consider a continuous-time optimization method based on a dynamical system, where a massive particle starting at rest moves in the conservative force field generated by the objective function, without any kind of friction. We formulate a restart criterion based on the mean dissipation of the kinetic energy, and we prove a global convergence result for strongly-convex functions. Using the Symplectic Euler discretization scheme, we obtain an iterative optimization algorithm. We have considered a discrete mean dissipation restart scheme, but we have also introduced a new restart procedure based on ensuring at each iteration a decrease of the objective function greater than the one achieved by a step of the classical gradient method. For the discrete conservative algorithm, this last restart criterion is capable of guaranteeing a qualitative convergence result. We apply the same restart scheme to the Nesterov Accelerated Gradient (NAG-C), and we use this restarted NAG-C as benchmark in the numerical experiments. In the smooth convex problems considered, our method shows a faster convergence rate than the restarted NAG-C. We propose an extension of our discrete conservative algorithm to composite optimization: in the numerical tests involving non-strongly convex functions with $$\ell ^1$$-regularization, it has better performances than the well known efficient Fast Iterative Shrinkage-Thresholding Algorithm, accelerated with an adaptive restart scheme.},
	isbn = {1573-2894},
	url = {https://doi.org/10.1007/s10589-021-00332-0},
	author = {Alessandro Scagliotti and Colli Franzone, P.}
}
@booklet {2021,
	title = {Deep Learning Approximation of Diffeomorphisms via Linear-Control Systems},
	year = {2021},
	keywords = {FOS: Computer and information sciences, FOS: Mathematics, Machine Learning (cs.LG), Optimization and Control (math.OC)},
	doi = {10.48550/ARXIV.2110.12393},
	url = {https://arxiv.org/abs/2110.12393},
	author = {Alessandro Scagliotti}
}
@article {2021,
	title = {Equilibrium measure for a nonlocal dislocation energy with physical confinement},
	year = {2021},
	month = {2021},
	url = {https://doi.org/10.1515/acv-2020-0076},
	author = {Mora, Maria Giovanna and Alessandro Scagliotti}
}
