1. Analytical and numerical methods of finding of an optimum.

The main objective of optimization is finding of an extremum (a minimum or a maximum) of function of an optimality criterion. Finding of an extremum of function by perhaps various methods. The choice of this or that method of finding of an optimum is one of the most important stages of optimization. Methods of search of an optimum can be divided into the following groups:

• analytical methods;

• methods of mathematical programming.

The group of analytical optimization methods unites analytical search of an extremum of function, a method of multipliers of Lagrange, variation methods and the principle of a maximum. Analytical search of an extremum of function, set without restrictions for independent variables is the simplest, but is applied to tasks at which the optimized function has the analytical expression differentiated in all range of a research, and the number of variables is small.

The group of methods of mathematical programming includes: dynamic programming, linear programming and nonlinear programming.

Dynamic programming – an effective method of the solution of tasks of optimization of multistage processes. The method assumes breakdown of the analyzed process at a stage (in time or in space) - for example, the reactor in the cascade or a plate in a column. Consideration of a task begins with the last stage of process and the optimum mode is determined step by step.

Linear programming – a method for the solution of tasks of optimization with linear expressions for an optimality criterion and linear restrictions for area of change of variables. Similar problems are solved by iterative methods. These methods are used in case of optimum production planning in case of limited quantity of resources, for transport tasks, etc.

Methods of nonlinear programming unite various methods of the solution of optimum tasks: gradient, without gradient and accidental search. General for methods of nonlinear programming is that they are used in case of the solution of tasks with nonlinear optimality criterions. All methods of nonlinear programming are numerical methods of search type. Their essence consists in determination of set of the independent variables giving the greatest increment of the optimized function. This group of methods is applied as for determined, and stochastic processes.

Test questions

1. What are necessary the tasks of optimization of CTS this for the decision.

2. What optimality criterions of calculation of CTS exist.

3. What are used methods of analytical and numerical finding of an optimum?

THE LIST OF THE RECOMMENDED LITERATURE

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