By Ya. Z. Tsypkin
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Extra info for Adaptation and Learning in Automatic Systems
W. (1964). ” McGraw-Hill, New York. Middleton, D . (1960). ” McGrawHill, New York. F. (1962). ” Wiley (Interscience), New York. L. (1966). ” Sovyetskoe Radio, Moscow. 2. (1 966). Adaptation, learning and self-learning in automatic systems, Automat. Remote Contr. 27 ( l) , 23-61. A. (1958). , IRE Trm7s. Inform. Theory IT-4 (l), 3. 1 Introduction In this chapter we shall consider recursive algorithmic methods of solving optimization problems. These methods encompass various iterative procedures related to the application of sequential approximations.
2 Algorithmic Methods of Optimization 30 Fig. 9 Multistage algorithms can be given not only in recursive form but also in the difference form. 39) where it is assumed that Aoc[n]= c[n]. 37), we obtain S m=O p, A'"c[n - m] - c Tm[n]VJ Sl m= 1 and P-sl Fig. , /Imand Bm. We shall not write such a relationship, since we will not be using it. We can obtain the single-stage algorithms from the multistage algorithms for s = s1 = 1. 20), or J(c), we obtain the corresponding multistage search algorithms.
43) Due to their nature, the continuous algorithms cannot be written in the recursive form. Only the differential and the integral forms can exist. 43). Since the concept of a step for the continuous algorithms is meaningless, it is better to call them the algorithms of the first and the higher orders than the single-stage and multistage algorithms. The continuous algorithms can be realized on analog computers, and can be used in the solution of finite (algebraic, transcendental) equations. If the conditions of optimality are 32 2 Algorithmic Methods of Optimization considered as a system of finite equations, then many methods of solving finite equations can be considered as continuous algorithms of optimization.
Adaptation and Learning in Automatic Systems by Ya. Z. Tsypkin