01171nas a2200121   4500008004100000020001400041245007800055210006900133260001500202520075800217100002700975856004701002       2022                        eng d  a1573-869800aA Gradient Flow Equation for Optimal Control Problems With End-point Cost0 aGradient Flow Equation for Optimal Control Problems With Endpoin  c2022/07/073 aIn 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.1 aScagliotti, Alessandro  uhttps://doi.org/10.1007/s10883-022-09604-201965nas a2200157   4500008004100000020001400041245007400055210006900129260001500198300001400213490000700227520147900234100002701713700002001740856004701760       2022                        eng d  a1573-289400aA piecewise conservative method for unconstrained convex optimization0 apiecewise conservative method for unconstrained convex optimizat  c2022/01/01  a251 - 2880 v813 aWe 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.1 aScagliotti, Alessandro1 aFranzone, Colli  uhttps://doi.org/10.1007/s10589-021-00332-000518nas a2200133   4500008004100000245007800041210006900119653004300188653002100231653002900252653003900281100002700320856003700347       2021                        eng d00aDeep Learning Approximation of Diffeomorphisms via Linear-Control Systems0 aDeep Learning Approximation of Diffeomorphisms via LinearControl10aFOS: Computer and information sciences10aFOS: Mathematics10aMachine Learning (cs.LG)10aOptimization and Control (math.OC)1 aScagliotti, Alessandro  uhttps://arxiv.org/abs/2110.1239300408nas a2200109   4500008004100000245008400041210006900125260000900194100002600203700002700229856004200256       2021                        eng d00aEquilibrium measure for a nonlocal dislocation energy with physical confinement0 aEquilibrium measure for a nonlocal dislocation energy with physi  c20211 aMora, Maria, Giovanna1 aScagliotti, Alessandro  uhttps://doi.org/10.1515/acv-2020-0076