Wavelet multi-resolution approximation for multiobjective optimal control

<div><p>A new sequential method based on multi-resolution approximation is proposed for solving computationally expensive multi-objective optimization problems. A traditional strategy is to decompose a multi-objective optimization problem into a number of single-objective optimization problems, whereby the PF can be regarded as a function of weights. Therefore, it is very natural to use wavelet multi-resolution approximation techniques for setting weight vectors. In our framework, the sequential approach starts with sampling aggressive functions on the initial coarsest grid with a few collocation points; once a rough PF is obtained, new points are automatically added on the basis of an adaptive wavelet collocation method. Therefore, the PF can be approximated with a relatively small number of weights. The efficiency of our method is demonstrated on two examples: a typical multi-objective optimization problem and an expensive multi-objective control optimal problem.</p></div

Media 3: Wavelength dependence of electron localization in the laser-driven dissociation of H2+

Originally published in Optics Express on 19 December 2011 (oe-19-27-26359

Three-mass-spring system.

Three-mass-spring system.</p

Nondipole effects on the double-slit interference in molecular ionization by xuv pulses

The double-slit interference in single-photon ionization of the diatomic molecular ion $\mathrm{H}_2^+$ is theoretically studied beyond the dipole approximation. Via simulating and comparing the interactions of the prealigned $\mathrm{H}_2^+$ and the hydrogen atom with the xuv pulses propagating in different directions, we illustrate two kinds of effects that are encoded in the interference patterns of the photoelectrons from $\mathrm{H}_2^+$: (i) the photon-momentum transfer and (ii) the finite speed of light. While both effects could modify the maxima of the interference fringes, we show that the former one hardly affects the interference minima. Our results and analysis show that the interference minima rule out the influences of the photon-momentum transfer and, potentially, the multielectron effect, thus performing a better role in decoding the zeptosecond time delay for the pulse hitting one and the other atomic centers of the molecule

Media 1: Wavelength dependence of electron localization in the laser-driven dissociation of H2+

Originally published in Optics Express on 19 December 2011 (oe-19-27-26359

Media 4: Wavelength dependence of electron localization in the laser-driven dissociation of H2+

Originally published in Optics Express on 19 December 2011 (oe-19-27-26359

Distribution of the involved collocation points on each level.

Distribution of the involved collocation points on each level.</p

Distribution of wavelet coefficients.

<p>Distribution of wavelet coefficients.</p

Dyadic grids on [0, 1].

<p>Dyadic grids on [0, 1].</p

Approximation error of the optimal objectives.

<p>Approximation error of the optimal objectives.</p