Set Intersection Theorems and Existence of Optimal Solutions
نویسندگان
چکیده
منابع مشابه
Set Intersection Theorems and Existence of Optimal Solutions
The question of nonemptiness of the intersection of a nested sequence of closed sets is fundamental in a number of important optimization topics, including the existence of optimal solutions, the validity of the minimax inequality in zero sum games, and the absence of a duality gap in constrained optimization. We consider asymptotic directions of a sequence of closed sets, and introduce associa...
متن کاملSet Intersection Theorems and Existence of Optimal Solutions 1 by Dimitri
The question of nonemptiness of the intersection of a nested sequence of closed sets is fundamental in a number of important optimization topics, including the existence of optimal solutions, the validity of the minimax inequality in zero sum games, and the absence of a duality gap in constrained optimization. We consider asymptotic directions of a sequence of closed sets, and introduce associa...
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For a family F of sets, let ex(F) := {A : A is an extremal intersecting sub-family of F}. The Erd®s-Ko-Rado (EKR) Theorem states that {A ∈ ( [n] r ) : 1 ∈ A} ∈ ex( ( [n] r ) ) if r ≤ n/2. The Hilton-Milner (HM) Theorem states that if r ≤ n/2 and A is a nontrivial intersecting sub-family of ( [n] r ) then |A| ≤ |{A ∈ ( [n] r ) : 1 ∈ A,A ∩ [2, r + 1] 6= ∅} ∪ {[2, r + 1]}|; hence {{A ∈ ( [n] r ) :...
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بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی بیان شده اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2006
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-006-0003-6