Overall objectives:

1 - This course focuses on the study of theory and methods for solving nonlinear optimization problems, emphasizing the theoretical analysis, computational implementation, and experimental evaluation of the algorithms studied. The basic principles of the theory and the main algorithms for constrained and unconstrained optimization of differentiable functions and non-differentiable optimization are studied, as well as the fundamental theoretical aspects and some methods of global optimization, with emphasis on nature-inspired metaheuristic optimization algorithms. The learning outcomes include the knowledge of the theoretical foundations and the main mathematical and metaheuristic techniques of optimization, the use of MATLAB/Octave, Python and Julia as tools for numerical and symbolic computation and graphical visualization, the computational implementation and experimental evaluation of the algorithms studied, as well as the analysis and interpretation of the numerical results obtained.

Syllabus:

1 - Introduction to Optimization: optimality conditions, convexity, and duality.
2 - Programming languages and software for optimization problems.
3 - Unconstrained Optimization: theory and algorithms for unconstrained optimization of differentiable functions: one-dimensional search methods, Newton and quasi-Newton methods, descent methods, conjugate direction methods.
4 - Constrained Optimization: theory and algorithms for constrained optimization of differentiable functions: feasible direction methods, penalty methods, barrier methods.
5 - Non-Differentiable Optimization: subgradient method, cutting plane methods, bundle methods.
6 - Global Optimization: metaheuristic optimization algorithms: simulated annealing, genetic algorithms, particle swarm optimization and other swarm-based optimization algorithms, metaphor-less optimization algorithms.

Literature/Sources:

Bertsekas, D. P. , 2016 , Nonlinear Programming, 3rd ed. , Athena Scientific
Friedlander, A. , 1994 , Elementos de Programação Não-Linear , Ed. da UNICAMP
Sundaram, R. K. , 1996 , A First Course in Optimization Theory , Cambridge University Press
Tavares, L. V.; Correia, F. N. , 1999 , Optimização Linear e Não Linear - Conceitos, Métodos e Algoritmos, 2.ª ed. , Fund. Calouste Gulbenkian
Rao, S. S. , 2019 , Engineering Optimization: Theory and Practice, 5th ed. , Wiley
Izmailov, A.; Solodov, M. , 2020 , Otimização, Vol. 1: Condições de Otimalidade, Elementos de Análise Convexa e de Dualidade, 4.ª ed. , IMPA
Izmailov, A.; Solodov, M. , 2018 , Otimização, Vol. 2: Métodos Computacionais, 3.ª ed. , IMPA
Lee, K. Y.; El-Sharkawi, M. A , 2008 , Modern Heuristic Optimization Techniques , Wiley/IEEE Press
Bazaraa, M. S.; Sherali, H. D.; Shetty, C. M. , 2010 , Nonlinear Programming: Theory and Algorithms, 4th ed. , Wiley-Interscience
Bonnans, J. F.; Gilbert, J. C.; Lemarechal, C.; Sagastizabal, C. A. , 2006 , Numerical Optimization: Theoretical and Practical Aspects, 2nd ed. , Springer
Kelley, C. T. , 1999 , Iterative Methods for Optimization , SIAM
Pham, D. T.; Karaboga, D. , 2000 , Intelligent Optimisation Techniques , Springer
Ruszczynski, A. , 2006 , Nonlinear Optimization , Princeton Univ. Press
Venkataraman, P. , 2009 , Applied Optimization with MATLAB Programming, 2nd ed. , Wiley
Beck, A. , 2023 , Introduction to Nonlinear Optimization: Theory, Algorithms, and Applications with MATLAB, 2nd ed. , SIAM
Kochenderfer, M. J.; Wheeler, T. A. , 2019 , Algorithms for Optimization , MIT Press
Antoniou, A.; Lu, W. S. , 2021 , Practical Optimization: Algorithms and Engineering Applications, 2nd ed. , Springer
Nocedal, J.; Wright, S. J. , 2006 , Numerical Optimization, 2nd ed. , Springer
Okwu, M. O.; Tartibu, L. K. , 2021 , Metaheuristic Optimization , Springer

Assesssment methods and criteria:

Classification Type: Quantitativa (0-20)

Evaluation Methodology:
The teaching methodology includes lectures and problem-solving classes with the use of whiteboard, notebook and video projector, the execution of practical work, and a short practical project. The adopted evaluation methodology includes the completion of two individual written tests, practical work carried out individually, and the development of a practical project, carried out individually or in a group. More explicitly, the evaluation parameters include: a written test on topics 1 and 3 of the syllabus, with a weight of 25% in the final mark; a written test on topics 4 and 5 of the syllabus, with equal weight in the final mark; practical work on topics 3 to 6 of the syllabus, with a weight of 20%, and a project involving topics 3, 4 and 6 of the syllabus, with a weight of 30% of the final mark. In the reassessment examination period and in the special assessment period, the final grade is based on the final written exam.