PROGRAMMASOZII MATEMATI­KI

PROGRAMMASOZII MATEMATI­KI, sohai ilmi matematika, ki nazariya va usulhoi daryofti ekstremumhoi funksiyahoro hangomi ijro shudani baze shartho khatti va gayrikhatti meomuzad. Mundarijai «programmasozii matematiki»-ro intikhobi tartibi amalhoi halli mas­ala tashkil medihad.

Halli masalai programmasozii matematiki kh*-ro nuqtai optimali (vektor) menomand. Programmasozii matematiki az faslhoi zerin iborat ast:

p r o g r a mmasozii khatti, programmasozii barjasta (funksiyai matlub G(kh) va majmua halhoi imkonpaziri on G barjastaand); programm a s o z i i diskreti (halli masala tanho dar nuqtahoi dimkretii majmui G daryofta meshavad); programmasozii kvadrati (funksiyai F (kh) funk­siya» barjasta va kvadratist, majmui G bo yorii nobarobarihoi khattivu gayrikhatti muayyan karda meshavad); programmasozii stokhasti (in jo bar khilofi usulhoi programmasozii favquzzikr akhbori programmonidashavanda kharakteri tasodufi dorad). Hamai masalaho» nomburda doroi khosiyati umumiand: minimumi lokalii dilkhoh nuqtai optimali meboshad. Baroi masalahoi serekstremali khosiyati mazkur joiz nest. Asosi nazariyai programmasozii khatti, barjasta va kvadratiro teoremai Kuna-Takker tashkil medihad, ki on meyori mavjudiyati nuqtai optimalii kh*-ro muayyan me­kunad. Dar asosi in teorema usulhoi gunoguni iteratsioni bunyod karda shudaand. Dar Programmasozii matematiki usulhoi muhosibai masalahoi ekstremali (masalan, metodi proeksiyagiri) mavqei kalon dorad. Khususiyati usulhoi mazkur on ast, ki hangomi tatbiqi amalii onho az kompyuterho isti­foda burdan mumkin ast. Masalahoi programmasozii matematikiro dar sohahoi gunoguni khojagit khalq, ki rohhoi kutohi hisobro taqozo mekunand, istifoda mebarand.

Programmasozii matematiki chun fanni mustaqil dar solhoi 50 —70 asri 20 tashakkul yoft. Masalahoi Programmosozii matematiki dar halli bisyor masalahoi idorakuniyu plankashii prosesshoi istehsoli, loihpkashi va plankashii perspektivi chun vositai boetimod ahamiyati kalon paydo kard.

Ad.: Zukhoviskiy S. I., Avde­eva L. I., Lineynoe i vipukloe programirovanie, 2 nad. M., 1967.

T. Haitov H. Najmiddinov.