March 2014
Intermediate to advanced
412 pages
11h 16m
English
Content preview from Numerical Methods and Optimization
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210 Numerical Methods and Optimization: An Introduction
9.11. Given a simple undirected graph G =(V,E), a subset I ⊆ V of vertices
is called an independent set if no two vertices in I are adjacent to each
other. Prove that the maximum independent set problem, which is to
find an independent set of maximum size in G,isNP-hard.
9.12. Show that
¯
f(x)=min{0,Lx − ˆx
∞
− } in the proof of Theorem 9.5
is Lipschitz continuous with the constant L in the infinity norm, its
global optimal value is −, and it differs from zero only inside the box
B
= {x : x − ˆx
∞
≤ /L}.
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