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Mathematics programmers - Nakonechny S.I.

2.8.7. Zatsiklennya in the tasks of literary programming

Yak is brought to the fore, the optimal plan of tasks for linear programming can be in one of the kutovih points of the bagatrone rozv'yakiv, the number of which is scintillated, that, for the sake of rozv'yazuvannya tasks simplex method, for the criticality of crocs one can know the optimal plan for zaasuvati, But the task is not about exclusion. However, the monotony of a simplex algorithm is very small in the case of non-homogeneity of all the basic planes, which are rejected in the course of the algorithmic procedure.

Якщо при досідженні значен У симплексній таблиці існує кілька нових значень з-поміж , Then tse means that you can vibrate to turn on the basis of one more vector. There is an iteration of the simplex method of the prism to the virogenous support plan, in which at least one of the basic zmіnnyh dorivnyuatime zero.

Yaksho active basic plan will be virodzhenim, tobo one more longer than the old members of the basic system, do not need to enter into zero, then with a vignette, which is necessary on the offensive basis for the basis, the value of the value q will be zero, and then the member of the zero number. The otzhe, in the onset of iteration, is wedded to the basis of the redistribution, the prichomu vsi znachennya basestnykh zmіnnih in the offensive support plan to be filled without zmіn, tbtot znachennosti tsіlової functіії після проведення ітерації не зміниться.

Tse means, as soon as it is possible, not to lead up to the scarred value of the tsil'ovoy function. In such a time, the number of the initial number of actions to be drawn up, a plan that was earlier drawn back in the process of initiating tasks. Podal'shi ітерації, carried out analogously, bring before re-sorting the very basic pillars. Virodzheny plan - the cause of that, theoretically vinikayemoslivost nezinchennogo number of repeated novo-youliznovnost ітерацій, які not to steal rozv'yuku, tobto the procedure will not be calculated if the mother. Taku situatsiyu nazivayut zatsiklenyam . The cycle could be buno b uniknuti, zapamyatyuyuchi pivotnye plan, scho set the cycle, and not turn up to them. Prote, schob zabezpechiti unambiguity viboru vector, a kind of vidvitsya in the baseline, rozrobleno a number of special priymov. Naytsіkavishim of them є so titles e - method .

To the virgin plan, the summit of the plan is multiplied, and it is implanted in the nest in the hyperplane. Іnakshe kazuchi, one vertex is seen as a number of virodzhenim plans, which means zlittya kolkokh tops of the bagatogranika in one. Ідеe e - to the method of replacing the zatyclenia of the field in the rose vertices. In order to finish, obviously, to enter the number of places in the upper reaches of the yakıs іnші znachennya, one zrobiti tse so, shobo not bulo znovu kіlokh mіnіmalnikh spivvidnoshen at the approaching krotsi. In such a way that a task can be assigned to a task. Prote can easily be brought to you, but the optimal plan of the tasks is solved, and you are allowed to enter zero values, optimal optimal rozvjazok pochatkoy problems.

In practice, to introduce magnitudes, yakі - duzhe malimi - tse polinomi dovіlno small (close to zero) dodatnoy value e . Коефіцієнтами поліномів take koefіtsієnti with nevidomih (basic and neizisnih) vidpііdnogo рівняння, and degrees e- number of unknown, tobto for the active i- th рівняння маємо поліном вид:

Tsіlkom zrozumіlo, scho for be-yakih Mozhna vibrati e nastilki malim, scho zavzhdi , Bod dansi si with degrees e , vyaschimi vіd і- go, will be a high order of smallness at the time of the first . Внаслідок цього всі utоворені поліноми різнитимуться за размер.ю. In the optimal plan, it is necessary to allow, .

Zauvazhimo, scho in different pizdozri on mozhlivist zatsiklennya (vipadok, if pochatkavi basic plan of virodzheny) polnoi Mozhna oddazy dodati up to vlnyh sistemi sistemi obmezhen, vasledok chogo matimemo: .