171 research outputs found
A randomised non-descent method for global optimisation
This paper proposes novel algorithm for non-convex multimodal constrained
optimisation problems. It is based on sequential solving restrictions of
problem to sections of feasible set by random subspaces (in general, manifolds)
of low dimensionality. This approach varies in a way to draw subspaces,
dimensionality of subspaces, and method to solve restricted problems. We
provide empirical study of algorithm on convex, unimodal and multimodal
optimisation problems and compare it with efficient algorithms intended for
each class of problems.Comment: 9 pages, 7 figure
Efficient Numerical Methods to Solve Sparse Linear Equations with Application to PageRank
In this paper, we propose three methods to solve the PageRank problem for the
transition matrices with both row and column sparsity. Our methods reduce the
PageRank problem to the convex optimization problem over the simplex. The first
algorithm is based on the gradient descent in L1 norm instead of the Euclidean
one. The second algorithm extends the Frank-Wolfe to support sparse gradient
updates. The third algorithm stands for the mirror descent algorithm with a
randomized projection. We proof converges rates for these methods for sparse
problems as well as numerical experiments support their effectiveness.Comment: 26 page
Spin dynamics and magnetic-field-induced polarization of excitons in ultrathin GaAs/AlAs quantum wells with indirect band gap and type-II band alignment
The exciton spin dynamics are investigated both experimentally and
theoretically in two-monolayer-thick GaAs/AlAs quantum wells with an indirect
band gap and a type-II band alignment. The magnetic-field-induced circular
polarization of photoluminescence, , is studied as function of the
magnetic field strength and direction as well as sample temperature. The
observed nonmonotonic behaviour of these functions is provided by the interplay
of bright and dark exciton states contributing to the emission. To interpret
the experiment, we have developed a kinetic master equation model which
accounts for the dynamics of the spin states in this exciton quartet, radiative
and nonradiative recombination processes, and redistribution of excitons
between these states as result of spin relaxation. The model offers
quantitative agreement with experiment and allows us to evaluate, for the
studied structure, the heavy-hole factor, , and the spin
relaxation times of electron, s, and hole, s, bound in the exciton.Comment: 17 pages, 16 figure
- …