Responsible instructor: György Dósa, DSc (dosa.gyorgy@mik.uni-pannon.hu)
Part I, Linear Programming
1. Introduction. Optimization, types of problems, dimensions of problems, iterative algorithms and convergence.
2. Examples of linear programming (LP) problems, the basic properties of Lp-s, the main theorem of LP.
3. The primal simplex method, optimality conditions, multi-objective optimization, goal programming.
4. Duality in linear programming. Weak and strong duality theorems. The relationship between dual feasibility and primal optimality, the dual simplex algorithm.
5. Solving large-scale LP problems. Properties of large-scale problems, data structures, preprocessing techniques, treatment of degeneration, searching of a good initial base.
Part 2, Nonlinear Programming
6. Univariate unconstrained optimization problems and solution methods. Convexity, concavity, first- and second-order optimality criteria.
7. Methods of solving multivariable unconstrained problems. Gradient methods, Newton's method, method of conjugate directions.
8. Conditional optimization problems. General form, equality and inequality conditions, first-order necessary optimality conditions, second-order optimality conditions, Lagrange function, Kuhn-Tucker theorem.
9. Primal methods. Advantages of primal methods, method of feasible directions, active set methods.
Literature:
1. D. G. Luenberger and Y. Ye, Linear and Nonlinear Programming, 3rd ed, Springer 2008.
2. I. Maros, Operations Research I., Lecture Notes v1.4i, PE MIK, 2012.