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We discuss how these methods can be combined in gradient optimization using parametrization GROUP including the finite bandwidth of the control electronics. Aranburu , T. Heinzel , and J. Comparison of gradient-based and gradient-free optimization methods in an artificial landscape. The shaded blue triangles show the gradient-free method, Nelder-Mead. The solid orange line and the dotted red line are gradient-based algorithms steepest descent and BFGS, respectively.
The steepest descent exhibits the characteristic zigzag-type behavior, which BFGS avoids due to the inverse Hessian approximation. Nelder-Mead, steepest descent, and BFGS, respectively, use 45, 34, and 15 iterations for convergence.
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The infidelity as a function of the number of evaluations for each algorithm. The different algorithms are shown at the basis size or steps size where they performed the best see legend. The control is held constant after the vertical dashed line. The dotted line shows the median of the gradients taken at the start of the optimization. The robustness of the optimal solutions from each algorithm to rescaling of the self-interaction in Eq.
The robustness of the optimal solutions from each algorithm to rescaling of the potential coefficients in Eq. Comparison of the convergence behavior for different values of the self-interaction for each algorithm. Comparison of the convergence behavior for different values of the potential coefficients. Quantum optimal control in a chopped basis: Applications in control of Bose-Einstein condensates J.
Optimal control of complex atomic quantum systems | Scientific Reports
Aranburu, T. Heinzel, and J. Sherson Phys. A 98 , — Published 14 August Abstract We discuss quantum optimal control of Bose-Einstein condensates trapped in magnetic microtraps. Research Areas. Optimization problems Quantum control. Physical Systems. Bose-Einstein condensates Ultracold gases. Issue Vol. Unconstrained optimization: first order necessary conditions; second order conditions. Constrained optimization; the Lagrangian; first order necessary conditions,. Calculus of variations; the Lagrange problem; the Euler equation; the augmented lagrangian;. Calculus of variations and optimal control; the Hamiltonian function.
The Pontryagin minimum principle; necessary conditions; necessary and sufficient conditions. The regulator problem: the optimal regulator problem on finite time interval; the optimal regulator problem. The minimum time problem; the minimum time problem for steady state system. The armonic oscillator ; the double integrator.
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Textbooks available in the DIAG library. Anderson, J. Bruni, G. Di Pillo, "Metodi variazionali per il controllo ottimo", Aracne, How, Jonathan. Tuersday Room A6.
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Wednesday Room A6. Lecture 1 September 25 and Lecture 2 September 26, October 2, Lecture Applications October Lecture 4 October 24, 30, Lecture moon landing October Lecture 5 November 5.
Lecture 6 November 5,6,7. Reference material.
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