Mathematical Optimization

Volledige vakbeschrijving

Mathematical Optimization is the subject of finding the best or optimum solution to a problem from a set of potential or feasible solutions. This course treats two different areas of optimization: nonlinear optimization and combinatorial optimization. Together these areas cover a wide range of real life optimization problems. Non-linear optimization deals with the situation in which there is a continuum of available solutions. The optimal solution is then usually approximated with one of several general purpose algorithms, such as Newton, quasi-Newton and conjugate gradient methods for unconstrained problems, and sequential quadratic programming and interior-point methods for general constrained problems. Combinatorial optimization deals with situations in which a best solution from a finite number of available solutions must be chosen. A variety of techniques, such as linear programming, branch and bound, Lagrange relaxation and approximation algorithms are employed to tackle these types of problems. In this course there will be a strong emphasis on practical problems, including in-class computer demonstrations and homework problems covering important cases of practical interest. After completing this course the student will have obtained a strong foundation in nonlinear and combinatorial optimization. The student will know the advantages/disadvantages of different methods and choose an appropriate method for a given problem. The student will know how to solve a variety of general optimization problems and operate adequately and independently in the domain of optimization.