CSEN 1048

4 lecture hours


5  ECTS credits

Mathematical Optimization

Abstract

  • Mathematical optimization is an abstraction of the problem of making the best possible from all allowed choices. We face the challenge of making an optimal decision is almost every scientific based field. Applications are many, some of them are: Data fitting, portfolio optimization, minimizing cost, maximizing profit, finding the shortest path... This course focus on single objective functions and more on continuous variables, while it touches only small family of optimization algorithms for discrete variables. The first part of this covers unconstrained optimization. We start with a single variable and we introduce gradient based methods and non-gradient methods. We next extend those notions to problems of n-variables. We next cover global optimization methods such as simulated annealing and genetic algorithms. The second part covers constrained optimization. We start by linear problems, next we introduce non-linear methods such as Lagrange and KKT method. In the third and last part of this course we covers some of the most famous discrete optimization algorithm applied to vision and machine learning.

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