| Ementa/Descrição: |
This course teaches basic and advanced optimization concepts for both deterministic and nondeterministic programming models. The GAMS software will be used to solve the examples, but the participants may use their preferred platform (AMPL, Python, Julia, exc.). First, we focus on linear programming (LP) problems, which are the most welcomed models in the industrial sector. We demonstrate how to model such problems, how to solve it, and how to analyze the results. We start with a very simple example, and then, the model will be developed step by step to cover all the concepts such as sensitivity analysis, LP duality, and bilevel programming. In this part, the participants will learn how to implement a bi-level model that covers the most timely and upcoming problems in Power and Energy Systems based on Game Theory approaches. Then, the main sources of disjoint decision-making variables are explained, and like the LP problems, detailed information on modeling, solution approaches, and ressult analysis related to the mixed-integer LP (MILP) problems are provided. The same problem will be udes to develop a MILP and mixed-integer nonlinear programming (MINLP). Convex programming as an effective approach for finding the global solution, even in nonlinear models will be explained. We will learn how to determine the convexity or concavity of a model and how to convexify some common nonconvex terms. To address the uncertainties in Energy and Power system problems, stochastic programming is introduced. An Energy Market example is provided for stochastic programming. |
| Referências: |
[1] Mokhtar S. Bazaraa, John J. Jarvis, Hanif D. Sherali, Linear Programming and Network Flows, 2010. [2] Ramteen Sioshansi, Antonio J. Conejo, Optimization in Engineering. Models and Algorithms, 2017. [3] Antonio J. Conejo, Miguel Carrión, Juan M. Morales, Decision Making Under Uncertainty in Electricity Markets, 2010. [4] Andreas Lundell, Joakim Westerlund & Tapio Westerlund, Some transformation techniques with applications in global optimization, 2007. |
