Sthochastic variational analysis applied to the energy industry

Abstract

Stochastic systems are challenging in mathematical optimization but they also have proven to be important in applications in Engineering, Economy, energy networks, and signal processing, for example. In this context the use of Stochastic Variational Analysis techniques have be proven to be important in the solution of generalized equations, optimization, and equilibrium whenever uncertainty is present. In this project we want to use the tools from Stochastic Variational Analysis in two important problems. First, we want to study the generalization of the continuous trajectories generates by differential inclusions associated with gradient and stochastic gradient descent to deal with the case of epsion-subgradients, with epsilon strictly greater than zero and still be able to analyze the convergence of the trajetories using Lyapunov ideas. Second, we want use variational ideas to derive new decomposition strategies for two stage stochastic problems where the presence of a risk measure precludes the use of traditional methods like progressive hedging. The idea is to derive new methods based on ADDM and variations focusing on problems that arise in the energy sector. (AU)