Advanced Topics in Optimization

This course introduces both theory and numerical methods for nonlinear programming. The goal is to provide students with solid foundations to deal with a wide variety of large-scale continuous optimization problems arising in Engineering and data science. The following algorithms are studied: dual-decomposition methods, interior-points method, Nesterov accelerated gradient descent, Alternating Direction Method of Multipliers (ADMM). The second part of the course introduces the metamodeling. The metamodeling approach approximates computation-intensive function (e.g., the output of a large-scale simulation code) by a simple analytical function, called metamodel. The second part is therefore devoted to the building of a metamodel from an expensive function, and the benefits in terms of parallel computation.