Classification Analytical methods classical methods

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Presentation transcript:

Numerical optimization methods Gintarė Viščiūtė Department of Applied Mathematics

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

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

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

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

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

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

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

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

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.

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?