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By Ya. Z. Tsypkin

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20 Certain Problems The most important problems faced in the development and application of the algorithms of optimization are to guarantee the convergence and to improve the methods of accelerating the convergence. It would also be very useful to develop a certain principle for a comparison of various optimization algorithms. This problem might be solved if we could find a general expression for the functional of the vector c[n]such that its minimization would lead to a uniquely defined step y[n].

The information can be either sufficient or insufficient for the information and solution of an optimization problem. , they can be written in explicit form. In the case of insufficient a priori information, the necessary facts about the criterion of optimality and/ or about the constraints are not complete. Since random variations always exist in realistic situations, a priori information becomes unreliable and inaccurate. , the amount, of a priori information plays a substantial role in the formulation and the solution of an optimization problem.

Or a random process {x(t); 0 I t < 0 0 ) . 2) in the averaging procedure (time or ensemble averaging), are equivalent. This means that the expressions of these functionals will always coincide if we can obtain them in an explicit form. 2). 12) The criteria of optimality have, or at least should have, a certain definite physical or geometrical meaning. For instance, in the automatic control systems the criterion of optimality represents a certain measure of deviation from the desired or prescribed system.

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