sun`iy bazis usuli

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5-mavzu. sun`iy bazis usuli tayanch so`z va iboralar: sun`iy bazis; sun`iy bazis usuli; kengaytirilgan masala; aynigan chiziqli programmalashtirish masalasi; aynigan reja (yechim); sikllanish, -usul. dars rejasi 1. sun`iy bazis, sun`iy vektor. 2. sun`iy bazis vektor usulining mohiyati. 3. sun`iy bazis vektor usulida bazis yechimning optimallik sharti. 4. -usul. chpm masalasi quyidagi ko`rinishda bo`lsin: (1) bu masalada tenglamalar istemasi keltirilmagan. shu sababli undagi tenglamalarga sun`iy o`zgaruvchilar kiritib uni kengaytirilgan sistemaga aylantiramiz. u holda quyidagi masala hosil bo`ladi: (2) bu yerda, yetarlicha katta musbat son. sun`iy bazis o`zgaruvchilariga mos vektorlar «sun`iy bazis vektorlar» deb ataladi. berilgan (1) masalaning optimal yechimi quyidagi teoremaga asoslanib topiladi. 1-teorema. agar kengaytirilgan (5.2) masalaning optimal yechimida sun`iy bazis o`zgaruvchilari nolga teng bo`lsa, ya`ni: tenglik o`rinli bo`lsa, u holda bu yechim berilgan (5.1) masalaning ham optimal yechimi bo`ladi. agar kengaytirilgan masalaning optimal yechimida kamida bitta sun`iy bazis o`zgaruvchi noldan farqli bo`lsa, u holda boshlang`ich masala yechimga ega bo`lmaydi. …

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an kamida bittasi nolga teng bo`lsa, chiziqli programmalashtirish masalasi aynigan chiziqli programmalashtirish masalasi deyiladi va bazis vektorlarga mos keluvchi bazis reja esa aynigan reja bo`ladi. yuqorida, simpleks usulni asoslash jarayonida chiziqli programmalashtirish masalalarini aynumagan deb faraz qilgan edik. bu farazga ko`ra simpleks usulning har bir iteratsiyasidan so`ng chiziqli funksiyaning qiymati kamaya borishini va chekli sondagi iteratsiyadan so`ng u o`zining optimal qiymatiga erishishi mumkinligini ko`rsatgan edik. agar masalaning bazis rejasi aynigan reja bo`lsa, (4) bo`lishi mumkin. u holda bir bazis rejadan ikkinchisiga o`tganda, chiziqli funksiyaning qiymati o`zgarmaydi. ba`zan bunday masalalarni yechish jarayonida sikllanish holati, ya`ni ma`lum sondagi iteratsiyadan so`ng oldingi iteratsiyalardan birortasiga qaytish holati ro`y berishi mumkin. sikllanish holati ro`y bergan masalalarda optimal reja hech qachon topilmaydi. sikllanish odatda, bazis rejadagi birdan ortiq bo`lgan holatlarda ro`y berishi mumkin. birdan ortiq vektorlar uchun bo`lganda bazisdan chiqariladigan vektorni to`g`ri aniqlash sikllanish holatini oldini olishda katta ahamiyatga egadir. bundan ko`rinadiki, aynigan masalalarni yechishga moslashtirilgan …

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ning qavariq kombinatsiyasi orqali ifodalash mumkin bo`ladi. vektorni qavariq konusning ichiga siljitish uchun ixtiyoriy kichik son olib, vektorlarning kombinatsiyasini tuzamiz va uni masalaning cheklamalarining o`ng tomoniga qo`shib yozamiz: (5) hosil bo`lgan vektor vektorlardan tashkil togan qavariq konusning ichida yotadi (1- shakl). demak, p0 ni vektorlarning qavariq kombinatsiyasi orqali ifodalash mumkin. xuddi shuningdek, umumiy holda berilgan masalaning (6) cheklamalarini quyidagicha yozish mumkin: (7) faraz qilaylik, bazis vektorlar bo`lib, ular matritsani tashkil qilsin. u holda (8) berilgan masalaning yechimi va (9) o`zgartirilgan (5.5) chegaralovchi shartli masalaning yechimi bo`ladi. (10) tenglik o`rinli bo`lgani uchun (8) ni ushbu ko`rinishda ifodalash mumkin. (11) demak, sistemaning o`ng tamoni quyidagicha aniqlanadi: (12) (13) kichik son bolgani uchun . simpleks usulini qo`llash jarayonida bazisdan chiqariladigan vektorni aniqlash uchun (14) formuladan foydalanamiz. farazga asosan nisbat da minimumga erishadi. agar qiymat, indeks uchun o`rinli bo`lsa, u holda bazisdan chiqariladi. bazisga kiritiladigan tanlangandan so`ng, simpleks jadval ma`lum yo`l bilan almashtiriladi. natijada …

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on bo`lib, uni shunday tanlash mumkinki, natijada tenglamalarning o`ng tomoniga ning faqat birinchi va ikkinchi darajasini qo`shish etarli bo`lsin. masalani simpleks jadvalga joylashtirib yechamiz: i. 150 6 0 0 0 0 0 0 1 1/4 1/2 0 -60 -90 0 -1/25 1 9 3 0 1 0 0 0 1 0 0 0 1 0 3/4 -150 -6 0 0 0 ii. -3/4 0 0 1 1 0 0 -240 30 0 -4/25 3/50 1 36 -15 0 4 -2 0 0 1 0 0 0 1 0 30 7/50 -33 -3 0 0 iii. -3/4 150 0 1 1 0 0 40 1 0 8/25 1/500 1 -84 -1/2 0 -12 -1/15 0 8 1/30 0 0 0 1 0 0 2/25 -18 -1 -1 0 iv. -3/4 0 1 0 0 -160 500 -500 0 1 0 -4 -250 250 -4/3 -100/3 100/3 8/3 50/3 -50/3 0 0 …

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5-mavzu. sun`iy bazis usuli tayanch so`z va iboralar: sun`iy bazis; sun`iy bazis usuli; kengaytirilgan masala; aynigan chiziqli programmalashtirish masalasi; aynigan reja (yechim); sikllanish, -usul. dars rejasi 1. sun`iy bazis, sun`iy vektor. 2. sun`iy bazis vektor usulining mohiyati. 3. sun`iy bazis vektor usulida bazis yechimning optimallik sharti. 4. -usul. chpm masalasi quyidagi ko`rinishda bo`lsin: (1) bu masalada tenglamalar istemasi keltirilmagan. shu sababli undagi tenglamalarga sun`iy o`zgaruvchilar kiritib uni kengaytirilgan sistemaga aylantiramiz. u holda quyidagi masala hosil bo`ladi: (2) bu yerda, yetarlicha katta musbat son. sun`iy bazis o`zgaruvchilariga mos vektorlar «sun`iy bazis vektorlar» deb ataladi. berilgan (1) masalaning optimal yechimi quyidagi teoremaga asoslanib ...

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