Intelligent Optimization Methods

This cours is intended as an  introduction to the theory of Optimization Methods for students in engineering. The cours consists of 15 two-hours lectures during which the presented topics are the following:

1. Problem formulation - the notion of objective function, constraints and feasible region, types of optimization problems.
2. LP - Linear Programming - analytic and matrix form of LP, the notion of dual linear programming DLP, the von Neumann Weak and Strong Dual Rules and their applications, introduction to the Simplex Method.
3. NLP - Nonlinear Programming - convex and concave functions, necessary and sufficient conditions and constrained NLP, introduction to numerical methods.
4. Discrete optimization - tree and network representation, review of numerical methods.
5. Optimization under uncertainty - types of problems, uncertaintly analysis and sampling.

References

1. URMILA DIWEKAR, Introduction to Applied Optimization, Springer 2008

2. Hamdy A. Taha, Operations research: An Introduction, Pearson Prentice Hall 2007

3. R. Fletcher, Practical Methods of Optimization, Wiley 2000

4. G.B. Dantzig, M.N. Thapa, Linear Programming 2:Theory and Extensions, Springer 2003

Lists of tasks and problems:

IOM1    IOM2   IOM3  IOM4 IOM5  IOM6  IOM7 IOM8  IOM9