The first course of Numerical Methods and Optimization deals with introducing basic topics in both fields. The course is mainly about the linear problems – the question of nonlinearity will be studied in the second course. The main topics discussed in the numerical method parts are classical and floating point error analyis, norms of vectors and matrices, calculations with vectors and matrices and different solution methods of linear systems.To make the learning procedure even more effective, we will provide a detailed description for the students on how to make operations with vectors and matrices in Excel. In addition, the MATLAB source codes will be found in each chapter, which will give an opportunity for you to effectively solve the exercises and problems not only manually, but with the help of a computer too.
The most typical problem in the theory of optimization is the maximization or minimization of an objective function subject to a number of constraints. In a special class of optimization problems the objective function and all the constraints are linear. These kinds of problems are called linear programming problems, or simply LP problems. Small LP problems of two variables can be solved graphically, after plotting the set of feasible solutions in two-dimensional space. General LP problems need more efficient solution methods, and one of them, the simplex algorithm, will be introduced. The transportation problem, which is a special LP problem, is also discussed. We study one of the nonlinear models as well: the linear-fractional programming problem. Its objective function is not linear, but the problem can be converted into an LP problem, and after this transformation it can be solved by the simplex method. The last chapter of the course gives instructions about computer-aided solutions of the discussed problems. For this purpose we use the SOLVER tool, which is an add-in component in Microsoft Excel. We hope you will find this course useful for modeling and solving practical problems, and you will continue your studies with the second course.
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Qualification: mathematician, University of Debrecen, 2003. Current employment:University of Miskolc, Department of Applied Mathematics. Scientific degree: PhD, mathematics and computer science (probability theory and mathematical statistics), 2011. Teaching skills: probability theory, mathematical statistics, numerical methods, optimization, programming theory.
