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Mathematics programmers - Nakonechny S.I.

8.7. Spoiled programmed

Opukle programvannya rozglyadaє the method of rozv'yazuvannya tasks nelinіynogo programvannya, mathematicheskie model yakikh mіstyat opulklі abo yunuti funktsii.

Obogal vizyad tasks and a flawed programvannya such:

, (8.31)

, ; (8.32)

, (8.33)

De , - Ugnet functions.

Analogic Viglyada is the problem for the function of the function.

Significantly: , Тоді , І маємо:

, (8.34)

; (8.35)

, (8.36)

De , - Functionality.

Oskills are problem-free, then the problem (8.31) - (8.33) is below the problem.

The multiplicity of admissible plans of tasks, that is, the system (8.32), is omitted.

Yak naslidok theorems 8.2 and 8.3 cope with such solidarity: the point of local maximum (minimum) of problems and the degenerate program (8.31) - (8.33) одно one-hour її global maximum (the minimum).

Separate, yakshcho vyzacheno a point of local ekstremumu tasksi and otklogo programvannya, then tse znacha, sho ozaydeno point global maximum (minimum).

In the case of interchange-nerves, the problem of a flawed program is rooted out, the method of Lagrange multipliers is stuck.

The Lagrange function for problems (8.31) - (8.33) is a form:

(8.37)

De - Lagrange multipliers.

The Vicorian theorem of the Kuhn-Tucker theorem, which is necessary to obtain the optimal solution of the problems and the flawed programming.

Theorem 8.4. The problem of nonlinear programming is given by the form (8.31) - (8.33), de functions Differential and curvilinear in X , then in order that the vector Був розв'язком цієї задачі, необхідно і достатньо, щоб інунув таким vector , The pair ( , ) Of a boolean binary point of the Lagrangian function, that is,

(І) , ; (8.38)

(II) , ; (8.39)

(ІІІ) , ; (8.40)

(IV) , . (8.41)

For tasks in the field of minerals (8.34) - (8.36), all functions Differentials and deformations in X, maemo umovi, analogue vizvedenenim, ali zi sign "≥" in the singularities (8.39) and (8.41).

The theorem is formulated in an addendum to the hypothesis of the witches of the theorems of both those and other paragraphs.