Generalized Homotopy Approach to Multiobjective Optimization

This paper proposes a new generalized homotopy algorithm for the solution of multiobjective optimization problems with equality constraints. We consider the set of Pareto candidates as a differentiable manifold and construct a local chart which is fitted to the local geometry of this Pareto manifold. New Pareto candidates are generated by evaluating the local chart numerically. The method is capable of solving multiobjective optimization problems with an arbitrary number k of objectives, makes it possible to generate all types of Pareto optimal solutions, and is able to produce a homogeneous discretization of the Pareto set. The paper gives a necessary and sufficient condition for the set of Pareto candidates to form a (k-1)-dimensional differentiable manifold, provides the numerical details of the proposed algorithm, and applies the method to two multiobjective sample problems.     

Classical and quantum dynamical regimes in the bound space projected dynamics of strongly driven H Rydberg atoms

The bound space projected dynamics of the one dimensional model of H Rydberg atoms subjected to strong microwave radiation exhibits three dynamical regimes:(i) perturbatively localized,(ii) chaotic,(iii) external field dominated. This classification holds classically as well as quantum mechanically. The spectral properties of the bound space projected dipole operator dominating regime(iii) are studied analytically. A semiclassical analysis shows that its eigenfunctions, projected on the unperturbed basis states |n〉 of the one dimensional model, decay liken ^?7/3.