This paper presents an extension of stochastic gradient descent for the minimization Lipschitz continuous loss functions. Our motivation is use in non-smooth non-convex optimization problems, which are frequently encountered applications such as machine learning. Using Clarke $$\epsilon $$ -subdifferential, we prove non-asymptotic convergence to approximate stationary point expectation proposed...

We construct a generalized gradient approximation of the exchange-correlation energy that satisfies the nonuniform scaling in one dimension and is accurate in the whole quasi-two-dimensional (Q2D) regime. Using spatial and energetic analyses of metal (111) surfaces, we show that the Q2D behavior is important at the surface of most transition metals, and that the here proposed Q2D-generalized gr...

This paper presents the method we used in the prediction challenge organised by the Sports Analytics Lab of the KU Leuven for the European football(soccer) championship. We built a generalised linear model to predict the score of a match. This score was modelled as the joint probability of a Poisson distribution, representing the total number of goals, and a binomial distribution, representing ...

The Conjugate Gradient (CG) method is often used to solve a positive definite linear system Ax = b. This paper analyzes two hard cases for CG or any Krylov subspace type methods by either analytically finding the residual formulas or tightly bound the residuals from above and below, in contrast to existing results which only bound residuals from above. The analysis is based on a general framewo...

in the present work, the electronic properties of titanium were studied in three phases of α, β and ω using the density function theory (dft). the full potential augmented plane wave plus local orbital (flapw+lo) method was applied using the generalized gradient approximation. the calculated total energies showed that omega phase was more stable than the two other phases. the largest electrical...

The adiabatic connection can be used in density functional theory to define the unknown ~exchange and! correlation density functional. Using conventional wave-function techniques, accurate estimates of thus defined ~exchange and! correlation energy densities can be obtained for specified systems. In this paper, numerical results are presented for the He and the Be atom, as well as the isoelectr...