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Sthochastic variational analysis applied to the energy industry

Grant number: 19/20023-1
Support type:Scholarships in Brazil - Doctorate
Effective date (Start): March 01, 2020
Effective date (End): February 28, 2023
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Principal researcher:Paulo José da Silva e Silva
Grantee:Felipe Eduardo Atenas Maldonado
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated research grant:13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID
Associated scholarship(s):22/02208-7 - Contemporary variants of splitting methods for large-scale optimization, BE.EP.DR

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)

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