1. Numerical optimization methods Gintarė Viščiūtė Department of Applied Mathematics

2. Classification Analytical methods classical methods
mathematical programming
liner programing
nonliner programing
game theory
Heuristic methods

3. Optimization problem Generic minimization problem where
X is the search space
f(x) objective function
the value f(x*) is the minimum

4. Local vs. global minimum, ,
Local minimum
Global minimum
Local minimum
Global minimum

5. Optimality conditions
Necessary conditions for optimality
Sufficient conditions for optimality
Gradient of the function is zero
Hessian matrix - positive definite

6. Optimization methods without limitations
Gradient method
Newton method
Reliable field methods
Variable metric methods
Conjugate direction methods

7. Nonlinear programming
Fines and barrier methods
Methods of allowable directions
Gradient projection and reduction methods
Lagrange function method

8. Linear programming Geometric interpretation Simplex method
Ellipsoid method
Interior-point methods

9. Mathematical programming applications
Production Planning
Agriculture
Distribution of resources
Transport Planning
Schedules
Economic, Finance
Human behavior modeling
Chemical Technology

10. Conclusion
There is no universal optimization method for resolving any task effectively.
Initial value selection has a significant influence for the minimum value of the found function.
Optimization techniques and its software is being actively developed branch of science.
Recently, the genetic algorithms are especially popular in optimization problems.

11. Thank you for your attention
Define local and global minimum.
Necessary and sufficient conditions for a minimum.
Differences between linear and nonlinear programming.
Formulate the optimization problem of your own practice.
Philosophical task. Who is better for optimization: a computer or a human?