DETERMINATION OF EDGES OF A CONVEX POLYTOPE

Cilt: 1 Sayı: 2 4 Temmuz 2011
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DETERMINATION OF EDGES OF A CONVEX POLYTOPE

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In this paper, the problem of determination of the edges of a convex polytope is considered. It is shown that this problem is equivalent to the standard linear programming problem and therefore can be solved by the simplex method. Further, for a special type of polytopes which are an affine transformation of a box we show that extremal points determine edges

Anahtar Kelimeler

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Kaynakça

  1. Barmish, B.R. (1994). New Tools for Robustness of Linear Systems, MacMillan, New York.
  2. Bartlett, A.C., Hollot, C.V. and Huang, L. (1988). Root locations of an entire polytope of polynomials: It suffices to check the edges, Mathematics of Control, Signals and Systems 1, 61-71.
  3. Bhattacharyya, S.P., Chapellat, H. and Keel, L.H. (1995). Robust Control: The Parametric Approach , Prentice Hall, New Jersey.
  4. Dullá, J.H., Helgason, R.V. and Hickman, B.L. (1992). Preprocessing schemes and a solution method for the convex hull problem in multidimensional space, in: O. Balci (ed.), Computer Science and Operations Research: New Developments in their Interfaces, Pergamon, Oxford.
  5. Dullá, J.H. and Helgason, R.V. (1996). A new procedure for identifying the frame of the convex hull of a finite collection of points in multidimensional space, European Journal of Operational Re- search 92, 352-367.
  6. Fukuda, K. (2004). From the zonotope construction to the Minkowski addition of convex polytopes, Journal of Symbolic Computation 38, No. 4, 1261-1272.
  7. Grünbaum, B. (2003). Convex Polytopes, Springer, New York.
  8. Murty, K.G. (2009). A problem in enumerating extreme points, and an efficient algorithm for one class of polytopes, Optim. Lett., 3, No. 2, 211-237.
  9. Papadimitriou, C.H. and Steiglitz, K. (1998). Combinatorial Optimization: Algorithms and Complexi- ty, Dover, New York.
  10. Pujara, L.R. and Bollepalli, B.S. (1994). On the geometry and stability of a polytope generated by a finite set of polynomials, American Control Conference, Baltimore, 236-237.

Kaynak Göster

APA
Büyükköroğlu, T. (2011). DETERMINATION OF EDGES OF A CONVEX POLYTOPE. Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi - B Teorik Bilimler, 1(2), 117-128. https://izlik.org/JA47TZ83CS
AMA
1.Büyükköroğlu T. DETERMINATION OF EDGES OF A CONVEX POLYTOPE. AUBTD-B. 2011;1(2):117-128. https://izlik.org/JA47TZ83CS
Chicago
Büyükköroğlu, Taner. 2011. “DETERMINATION OF EDGES OF A CONVEX POLYTOPE”. Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi - B Teorik Bilimler 1 (2): 117-28. https://izlik.org/JA47TZ83CS.
EndNote
Büyükköroğlu T (01 Ağustos 2011) DETERMINATION OF EDGES OF A CONVEX POLYTOPE. Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi - B Teorik Bilimler 1 2 117–128.
IEEE
[1]T. Büyükköroğlu, “DETERMINATION OF EDGES OF A CONVEX POLYTOPE”, AUBTD-B, c. 1, sy 2, ss. 117–128, Ağu. 2011, [çevrimiçi]. Erişim adresi: https://izlik.org/JA47TZ83CS
ISNAD
Büyükköroğlu, Taner. “DETERMINATION OF EDGES OF A CONVEX POLYTOPE”. Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi - B Teorik Bilimler 1/2 (01 Ağustos 2011): 117-128. https://izlik.org/JA47TZ83CS.
JAMA
1.Büyükköroğlu T. DETERMINATION OF EDGES OF A CONVEX POLYTOPE. AUBTD-B. 2011;1:117–128.
MLA
Büyükköroğlu, Taner. “DETERMINATION OF EDGES OF A CONVEX POLYTOPE”. Anadolu Üniversitesi Bilim Ve Teknoloji Dergisi - B Teorik Bilimler, c. 1, sy 2, Ağustos 2011, ss. 117-28, https://izlik.org/JA47TZ83CS.
Vancouver
1.Taner Büyükköroğlu. DETERMINATION OF EDGES OF A CONVEX POLYTOPE. AUBTD-B [Internet]. 01 Ağustos 2011;1(2):117-28. Erişim adresi: https://izlik.org/JA47TZ83CS