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Mathematical Programming I: Chapter 4 and Chapter 5

Summary: Mathematical Programming I:
Chapter 4 and Chapter 5
Sheets for the course, version: 22-05-2011
Georg Still
The script is part of the book:
Faigle/Kern/Still, Algorithmic principles of Mathematical
on: http://wwwhome.math.utwente.nl/stillgj/priv/
Math. Prog. Ch.4,5 p 1
4. Convex sets, convex functions
4.1 Convex sets
Recall the definitions of closed, compact sets P Rn.
Def. A set P Rn is called convex if
x, y P, [0, 1] x + (y - x) P
Ex 4.1 Any intersection of closed convex sets is a closed
convex set.
Def. Let H be a hyperplane H = {x | aT x = } (with some
0 = a Rn) and let P Rn, y / P. H is called a separating
hyperplane wrt. P and y if:


Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente


Collections: Engineering