Adaptation and Learning in Automatic Systems by Ya. Z. Tsypkin PDF

By Ya. Z. Tsypkin

ISBN-10: 0127020500

ISBN-13: 9780127020501

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An attempt to find the answer for a general case would be futile. The specific choice of these parameters depends on our definition of the best algorithms. The parameters in the algorithms of relaxation and many gradient methods are optimal with respect to the preselected criteria. Therefore, we obtain the algorithms which are locally” best at each step. Of course, this does not mean that the algorithm is the best overall. The problem of designing the best algorithms of optimization is very similar to the problems of synthesis for discrete or continuous systems which realize these algorithms.

A,) is still an unknown vector of Lagrange multipliers; T indicates the transport of a vector, and g(c) = ( g , ( c ) , . . ,g M ( c ) )is a vector function. 25) where is an N x A4 matrix. 25) by using the algorithms 2 Algorithmic Methods of Optimization 26 or 11 - r [ n ] V J ( ~ [-n 11 + G(c[~ - I]k[i? 28) The existence of equality constraints slightly complicates the structure of the system which corresponds to the algorithms of optimization. The special loops which define the Lagrange multipliers are introduced (Fig.

25) by using the algorithms 2 Algorithmic Methods of Optimization 26 or 11 - r [ n ] V J ( ~ [-n 11 + G(c[~ - I]k[i? 28) The existence of equality constraints slightly complicates the structure of the system which corresponds to the algorithms of optimization. The special loops which define the Lagrange multipliers are introduced (Fig. 7). Many Fig. 7 other algorithms of optimization which differ only according to the chosen Lagrange multipliers exist, but we shall not treat them here. 9 Constraints I1 The inequality constraints cannot be treated by the classical methods discussed thus far.

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Adaptation and Learning in Automatic Systems by Ya. Z. Tsypkin


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