Gradient projection methods based on the Barzilai-Borwein spectral steplength choices are considered for quadratic programming (QP) problems with simple constraints. Well-known nonmonotone spectral projected gradient methods and variable projection methods are discussed. For both approaches, the behavior of different combinations of the two spectral steplengths is investigated. A new adaptive steplength alternating rule is proposed, which becomes the basis for a generalized version of the variable projection method (GVPM). Convergence results are given for the proposed approach and its effectiveness is shown by means of an extensive computational study on several test problems, including the special quadratic programs arising in training support vector machines (SVMs). Finally, the GVPM behavior as inner QP solver in decomposition techniques for large-scale SVMs is also evaluated

This work deals with special decomposition techniques for the large quadratic program arising in training Support Vector Machines. These approaches split the problem into a sequence of quadratic programming subproblems which can be solved by efficient gradient projection methods recently proposed. By decomposing into much larger subproblems than standard decomposition packages, these techniques show promising performance and are well suited for parallelization. Here, we discuss a crucial aspect for their effectiveness: the selection of the working set, that is the index set of the variables to be optimized at each step through the quadratic programming subproblem. We analyse the most popular working set selections and develop a new selection strategy that improves the convergence rate of the decomposition schemes based on large sized working sets. The effectiveness of the proposed strategy within the gradient projectionbased decomposition techniques is shown by numerical experiments on large benchmark problems, both in serial and parallel environments.

Image deblurring, Scaled gradient projection method, Graphics processing units,

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Abstract. In this work we present TDStool, a general-purpose easy-to-use software tool for the solution of the time-dependent Schrödinger equation in 2D and 3D domains with arbitrary time-dependent potentials. The numerical algorithms adopted in the code, namely Fourier split-step and box-integration methods, are sketched and the main characteristics of the tool are illustrated. As an example, the dynamics of a single electron in systems of two and three coupled quantum dots is obtained. The code is released as an open-source project and has a build-in graphical interface for the visualization of the results. IntroductionThe astonishing development in semiconductor growth, characterization and processing technologies opened new horizons in the field of carriers control, up to the single electron level [1]. In fact, single-particle quantum interference is routinely achieved in advanced research laboratories and single electrons are not only confined, but also moved by varying electromagnetic fields [2]. The theoretical modeling of such systems is usually tackled with numerical instruments developed on a case-by-case basis. Although this allows for a great specificity, the development work is very expensive.Here we present a novel software tool for the numerical solution of the time-dependent (TD) Schrödinger equation. We named it TDStool and released it as an open-source project (binaries are available for Windows and Linux systems), free for non-commercial use [3]. The main characteristics of TDStool are: 2D and 3D solution domain; arbitrary TD electric potential landscape; uniform magnetic field; nonuniform (x-y-z separable) discretization grid; clean graphical user interface for input setup and results visualization; comprehensive documentation. Two different numerical algorithms are available, namely Fourier split-step and box-integration method.In addition to the linear Schrödinger case, the nonlinear system dynamics determined by TD Gross-Pitaevskii equation [4] can be simulated. In fact, many recent experimental results on the manipulation of quantum ultracold condensates exposed the quantum coherence of their dynamics [5] and confirmed the extra potential-like term g|ψ(r)| 2 in their equation of motion, proportional to the local particle density.In the next section we sketch the numerical algorithms adopted in the code. Then, in the remaining two sections, we present two examples of applications, namely the single-particle

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