Finite illumination of unbounded closed convex sets

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Finite Illumination of Unbounded Closed Convex Sets

If K is an unbounded closed convex subset of Ed having nonempty interior, we seek necessary and/or sufficient conditions to ensure that the boundary of K can be externally illuminated from a finite set of directions. This problem was stated as open in a recent book by Boltyanski. The tools used in this search are those developed by Visibility Theory such as the ideas of star, inner stem, visibi...

متن کامل

Connectedness of Solution Sets for Weak Vector Variational Inequalities on Unbounded Closed Convex Sets

and Applied Analysis 3 (ii) The scalar C-pseudomonotonicity in Definition 2 is weaker than C-pseudomonotonicity in Definition 1(ii). In fact, for any ξ ∈ C∗ \ {0}, x, y ∈ X, if ⟨ξ(u∗), y − x⟩ ≥ 0, then we have ⟨u∗, y − x⟩ ∉ − intC. Then, it follows from the Cpseudomonotonicity of T that ⟨V∗, y − x⟩ ∈ C, which implies that ⟨ξ(V∗), y − x⟩ ≥ 0. Definition 5. The topological space E is said to be c...

متن کامل

Unbounded Convex Semialgebraic Sets as Spectrahedral Shadows

Recently, Helton and Nie [3] showed that a compact convex semialgebraic set S is a spectrahedral shadow if the boundary of S is nonsingular and has positive curvature. In this paper, we generalize their result to unbounded sets, and also study the effect of the perspective transform on singularities.

متن کامل

Functionally closed sets and functionally convex sets in real Banach spaces

‎Let $X$ be a real normed  space, then  $C(subseteq X)$  is  functionally  convex  (briefly, $F$-convex), if  $T(C)subseteq Bbb R $ is  convex for all bounded linear transformations $Tin B(X,R)$; and $K(subseteq X)$  is  functionally   closed (briefly, $F$-closed), if  $T(K)subseteq Bbb R $ is  closed  for all bounded linear transformations $Tin B(X,R)$. We improve the    Krein-Milman theorem  ...

متن کامل

Unbounded convex sets for non-convex mixed-integer quadratic programming

This paper introduces a fundamental family of unbounded convex sets that arises in the context of non-convex mixed-integer quadratic programming. It is shown that any mixed-integer quadratic program with linear constraints can be reduced to the minimisation of a linear function over a set in the family. Some fundamental properties of the convex sets are derived, along with connections to some o...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: International Mathematical Forum

سال: 2006

ISSN: 1314-7536

DOI: 10.12988/imf.2006.06003