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Advanced nondifferentiable optimization techniques for hard structured optimization problems

Grant number: 17/05198-4
Support type:Scholarships abroad - Research Internship - Post-doctor
Effective date (Start): June 01, 2017
Effective date (End): May 31, 2018
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Principal Investigator:José Mário Martinez Perez
Grantee:Rafael Durbano Lobato
Supervisor abroad: Antonio Frangioni
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Local de pesquisa : Università di Pisa, Italy  
Associated to the scholarship:15/18053-9 - Study and implementation of deterministic methods for global optimization of nonlinear programming problems, BP.PD


Many energy optimization problems, such as the Unit Commitment (UC) one, possess several forms of spatial, temporal and logical structure that partition the decisions (variables) into distinct blocks. Hence they would decompose along these lines, were it not for some operational or logical conditions (linking constraints or variables) that relate decisions from different blocks. These problems are therefore particularly well-suited for decomposition approaches, such as these based on Lagrangian or Benders' methods. However, these are hard to implement, partly because of very limited support from standard modelling and solution tools. The aim of the project is to exploit the Structured Modelling System (SMS++), a C++ modelling environment that is currently being developed at the Department of Computer Science of the University, to implement generic decomposition-based solution approaches for different variants of UC. Thanks to the capabilities of SMS++, the approaches will be able to both work with general-purpose solvers and exploit the availability of specialized algorithms for specially-structured subproblems, thereby allowing to develop approaches that do not depend on the fine details of the model like the operational constraints of the generating units, that change a lot in different operating environment. Solving the corresponding large-scale nondifferentiable optimization problems will require improving upon the state-of-the-art techniques for this class of problems, using e.g. techniques like "easy components", structured decomposition, and inexact/incremental/asynchronous algorithms. (AU)

Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
BIRGIN, E. G.; LOBATO, R. D. A matheuristic approach with nonlinear subproblems for large-scale packing of ellipsoids. European Journal of Operational Research, v. 272, n. 2, p. 447-464, JAN 16 2019. Web of Science Citations: 1.

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