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Mathematics programmers - Nakonechny S.I.

1.6. Classification of problems of mathematical programming

In mathematic programming, two strains - deterministic tasks and stochastic ones . The deterministic tasks are not to disconnect the vipadkichnye zmіnichi chi parameterіv. Уся початкова інформація повністю it is noted. In the stochastic tasks, vikoristvuyutsya vhіdna іnformatsіya, yaka mіstit elementy neiznachenosty, abo igrokі parametri nabuvayut znachen vidpovidno to viznacheniy funktsii rozpodilu vypadkovykh magnitudes. Napriklad, yakshcho in the economy-mathematical model of vrozhajnostі sіlskogospodarskih cultures set by its mathematicheskim spodivanni, then such a task is deterministic. Yakshcho v vrozhaynosty prednazhni functitsіami rozpodilu, napriklad normal s matematicheskim spodivannyam a і dispersion D , then such a task is stochastic.

Yaksho u vidpovidnih ekonomichnih protsessah vypadkovі yavischa not vidіgryayut істотної ролі, then the problem can be rozv'yazuvati yak determinovanu. In this case, the economical and mathematical model of the ma- buti is stochastic, that is, it is the vipadkovi function and the magnitude. The structure of such tasks is such that they are wagging in the proximity of the rooted, so called stochastic programs .

Кожен з названих напрямків вклює ти type of problems of mathematical programming, yakі in your own worm поділяються на інші класи. Schematically, the classification of problems is shown in Fig. 1.2 (Sub-headings for deterministic tasks, ali vine same for i stochastic).

Fig. 1.2. Classification of problems of mathematical programming

Yak determinovany, so і stochastic tasks can be static (unicorn) abo dinamichnymi (bagatokrovikimi). Оскільки економічні processes are rozvivayutsya in chasі, відповідні економіко-математичні моделі мають відбражати їх динаміку. Ponyattya dynamichnosti povjazane zi zmіnami ob'ekta (yavishcha, protsentu) at chasі. On the other hand, it is possible to read about the plan for the development of the economy of Ukraine until 2005, then it is not enough for the macroeconomic indicators to show up in 2005, but on all industrial promises, tobto slid planuvati postupovist (dinamiku) rozvitku folk-prishodkih protsessiv. Such a plan is called strategic . In gnomu moe bouti obvruntovana optimal (nykrascha, ale real) traektorіya rozvitku people's government. Проте під впливом некерованиих чинників actual viewers shoroku mozhut vidhlyatisya vіd plannonovyh. To that it is necessary neobhіdnіst korjuguvati kozhny rіchny plan. So I plan to call tactful . Wongs are viznachayutsya in the result of rozv'yannya static ekonomiko-mathematical problems.

It is vitally important to assure vidmіnnіst mіzh one-th bagatokrokovymi tasks. Bagatokrokіist yak method rozv'yazvanya tasks mathematic programvannya zoumovlyuyutsya, nasampered, bahatovimіrnіstu problemі i znachaє, scho poslіdovno zastosovuči індукцію, krok krokom zapodyagit optimal znachennya multiply zmіnnih, prichomu otrimaniy na kozhnom krotsі rozv'yazok moe zadovolnyati otvi optimichnostі rozdnogo rozv'yuku. This procedure can be done in an hour. One-tasking tasks, navpacks, are characterized by a timetable, all components of the optimal task plan, and are assigned to the water algorithm for the rest of the algorithm (the rest of the cracks). Potrівно розрізняти ітераційність to the algorithm і yogo bagatokrokovі. On the other hand, the simplex method of isolating the tasks of linear programming is used to select the optimal plan for the first stage of the permissible plan and the result of the activity. Here it is impossible to integrate (crocs) an algorithm of the simplex method, but you can not interrupt it in the way of the economy of economy (yavishcha). Deykі tasks math programuvannya can rozglyadati yak one-abo bagatrokoki lay in the way iz rozv'yanya. Yakshto task can be rozv'yazuvati yak odnokrokovu, then rozv'yazuvati її yak bagatokrokovu nedotsilno, bo in such a time for the knowledge of the optimal plan neobhidno zastosovuvati folding method. Prote bil'shist ekonomichnyh protsessiv є dinamichnimi, їh parametr zminiyutsya v chasі zalajat vіd rіshen kerіvnitsvva, yakі be brought priymati with the method of rectification of the economy system for traektorієyu, yaka is indicated by the strategic plan.

The tasks of the mathematical program are to be taken on the discrete and non-pererial basis . Discrete nazyvayut tasks, in any one, kilka abo all zmіnnі nabuvayut lishhe discrete meaning. Z-pomizh them okremi type to become tasks, in which one abortion of zmіnnih nabuvayut tsilokshislovy znachen. Їх name tasks of numerical programming . Yaksho vs zmіnnі mozut nabuvati be-yakikh znachen on the active intervals of the numerical axis, then the task is non-reusable .

Oskilki in economical and mathematical models of solitude and imagery are described for the sake of functionality, then it is up to the view of the whole world to solve the problems of the problems on the basis of the linearity . Yaksho tsil'ova funktsiia (1.2) that obmezhennya (1.3) є lіnіynimi, toto mistjat zmіnnі xj tilki at the first zero degree, then this task is linear. In the past, there will not be a problem.

Naiprostіshimі з розглянутих типів є статичні, детерміновані, неперервні та лінійні задачі. The unversion method, which is called simplex method, is roughened by a pompous transgression of such tasks-those, for the sake of rozvjazuvannya. Theoretically, the task of solving the problem of linear programming is possible. For active types of linear tasks, but to muffle the special structure, distribute the special methods of isolation, and the effective ones. For example, the transport problem can be solved using the simplex method, albeit effective ones, special methods, application, method of potentialities.

Economical and technologic processes, as a rule, are non-linear, stochastic, rooted in the minds of unheeded. Lien economy-mathematical models are often inadequate, tobto such, it is inaccurate to describe the process, which is to be delivered, to be brought to the future by stochastic, dynamic, non-linear models. Розв'язувати такі задачі набагато складніше, ніж лінійні, оскільки неє universal to the method of їх розв'язання. For okremih types of non-linear tasks, special procedures for rozvianne are parsed. Prote Slid zazchachiti, scho on pracovitsi zastosovuyot, zdebilshogo, linniei ekonomiko-mathematicheskim model. Often non-linearity is approximated (nablizhayut) before lіnіynikh. Такий підхід є доволі ефективним.

In non-linear programming (in the course of functions, as in the economics and mathematics model), viocremlyuyut opacle is quadratic programmed. The task is to lie down to a spoiled program in this case, if the function is curved, it is not possible to maximize, but everything is of the same type, (≤) abo rivnyannya, in some parts of the world - opulent functions, and rights of the part - Steel quantities. At the same time, the type (≥) їх ліві частини мають бути вгнутими функціями. Тоді область допустимих планів є опуклою та існує global, єдиний екстремум. Quadratically programmed - yakshchoo tsil'ova function is quadratic, and obmezhenna linniny.

Shchuino Boole is a little more basic than the typical problems of mathematical programming. Can takozh for rіznimi visoki vitokremiti i іnshі підтипи. Tse osoblivo stosuyutsya problems lіnіynogo, nelinnіnogo i stokhachnogo programvannya. Napriklad, yak okremi type rozglyadayut shattered-linear programvannya , if obmezhennia є lіnіynimi, and tsil'ova funktsiya - shot-line. The special type is to become the tasks of the theory and the yak , to be widely stuck in the economy of economy. Adzhe here dityut dvi chi bіl more confliktnyh storin, yakі maiyut pokachovo abo ponnistyu protilezhnі tsіlі. In the course of the problems of the theory, with its own cherv, takozh viokremljuyut pevnі pіdtipi. Napriklad, igri dukh osib nezovoyu sumoju .

It is imposed a vital role in the tasks of the Vicoristan for the structure of the course "Mathematics programmers".