Continuous stage stochastic Runge–Kutta methods

Effective order strong stability preserving RungeKutta methods

We apply the concept of effective order to strong stability preserving (SSP) explicit Runge–Kutta methods. Relative to classical Runge–Kutta methods, effective order methods are designed to satisfy a relaxed set of order conditions, but yield higher order accuracy when composed with special starting and stopping methods. The relaxed order conditions allow for greater freedom in the design of ef...

Inexact Bundle Methods for Two-Stage Stochastic Programming

Stochastic programming problems arise in many practical situations. In general, the deterministic equivalents of these problems can be very large and may not be solvable directly by general-purpose optimization approaches. For the particular case of two-stage stochastic programs, we consider decomposition approaches akin to a regularized L-shaped method that can handle inexactness in the subpro...

Sequential Bounding Methods for Two-Stage Stochastic Programs

In rare situations, stochastic programs can be solved analytically. Otherwise, approximation is necessary to solve stochastic programs with a large or infinite number of scenarios to a desired level of accuracy. This involves statistical sampling or deterministic selection of a finite set of scenarios to obtain a tractable deterministic equivalent problem. Some of these approaches rely on bound...

Decomposition Methods for Two-Stage Stochastic Integer Programs

Fast Communication Two-stage Stochastic Runge-kutta Methods for Stochastic Differential Equations with Jump Diffusion