A PVT-TYPE ALGORITHM FOR MINIMIZING A NONSMOOTH CONVEX FUNCTION

A general framework of the (parallel variable transformation) PVT-type algorithm, called the PVT-MYR algorithm, for minimizing a nonsmooth convex function is proposed, via the Moreau-Yosida regularization. As a particular scheme of this framework an ε-scheme is also presented. The global convergence of this algorithm is given under the assumptions of strong convexity of the objective function and an ε-descent condition determined by an ε-forced function. An appendix stating the proximal point algorithm is recalled in the last section

Theoretical Analysis of Random Scattering Induced by Microlensing

Theoretical investigations into the deflection angle caused by microlenses offer a direct path to uncovering principles of the cosmological microlensing effect. This work specifically concentrates on the the probability density function (PDF) of the light deflection angle induced by microlenses. We have made several significant improvements to the widely used formula from Katz et al. First, we update the coefficient from 3.05 to 1.454, resulting in a better fit between the theoretical PDF and our simulation results. Second, we developed an elegant fitting formula for the PDF that can replace its integral representation within a certain accuracy, which is numerically divergent unless arbitrary upper limits are chosen. Third, to facilitate further theoretical work in this area, we have identified a more suitable Gaussian approximation for the fitting formula.Comment: 15 pages, 6 figures, accepted for publication in Research in Astronomy and Astrophysic

Bounding regret in empirical games

Empirical game-theoretic analysis refers to a set of models and techniques for solving large-scale games. However, there is a lack of a quantitative guarantee about the quality of output approximate Nash equilibria (NE). A natural quantitative guarantee for such an approximate NE is the regret in the game (i.e. the best deviation gain). We formulate this deviation gain computation as a multi-armed bandit problem, with a new optimization goal unlike those studied in prior work. We propose an efficient algorithm Super-Arm UCB (SAUCB) for the problem and a number of variants. We present sample complexity results as well as extensive experiments that show the better performance of SAUCB compared to several baselines

A superlinear space decomposition algorithm for constrained nonsmooth convex program

AbstractA class of constrained nonsmooth convex optimization problems, that is, piecewise C2 convex objectives with smooth convex inequality constraints are transformed into unconstrained nonsmooth convex programs with the help of exact penalty function. The objective functions of these unconstrained programs are particular cases of functions with primal–dual gradient structure which has connection with VU space decomposition. Then a VU space decomposition method for solving this unconstrained program is presented. This method is proved to converge with local superlinear rate under certain assumptions. An illustrative example is given to show how this method works

Deep Neural Network Representation of Density Functional Theory Hamiltonian

The marriage of density functional theory (DFT) and deep learning methods has the potential to revolutionize modern research of material science. Here we study the crucial problem of representing DFT Hamiltonian for crystalline materials of arbitrary configurations via deep neural network. A general framework is proposed to deal with the infinite dimensionality and covariance transformation of DFT Hamiltonian matrix in virtue of locality and use message passing neural network together with graph representation for deep learning. Our example study on graphene-based systems demonstrates that high accuracy ($\sim$meV) and good transferability can be obtained for DFT Hamiltonian, ensuring accurate predictions of materials properties without DFT. The Deep Hamiltonian method provides a solution to the accuracy-efficiency dilemma of DFT and opens new opportunities to explore large-scale materials and physics.Comment: 5 pages, 4 figure