In recent years, implicit stochastic Runge–Kutta (SRK) methods have been developed both for strong and weak approximations. For these methods, the stage values are only given implicitly. However, in practice these implicit equations are solved by iterative schemes such as simple iteration, modified Newton iteration or full Newton iteration. We employ a unifying approach for the construction of ...

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Quantum scattering at zero energy is studied with stochastic methods. A path integral representation for the scattering cross section is developed. It is demonstrated that Monte Carlo simulation can be used to compare effective potentials which are frequently used in multiple scattering with the exact result.

In this paper we study the problem of minimizing the average of a large number (n) of smooth convex loss functions. We propose a new method, S2GD (Semi-Stochastic Gradient Descent), which runs for one or several epochs in each of which a single full gradient and a random number of stochastic gradients is computed, following a geometric law. The total work needed for the method to output an ε-ac...

In this paper, we propose to enhance particle-based stochastic optimization methods (SO) by using Principal Component Analysis (PCA) to build an approximation of the cost function in a neighborhood of particles during optimization. Then we use it to shift the samples in the direction of maximum cost change. We provide theoretical basis and experimental results showing that such enhancement impr...

Stochastic programming is concerned with practical procedures for decision-making under uncertainty , by modelling uncertainties and risks associated with decisions in a form suitable for optimization. The eld is developing rapidly with contributions from many disciplines such as operations research, probability and statistics, and economics. A stochastic linear program with recourse can equiva...