For a given vector a E R" and scalar A > 0, show that the following problem 1 minx, ||x – all +A ||x||2 has the optimal solution if ||a||2 A. xopt def 0, 1 ||a|l2.
For a given vector a E R" and scalar A > 0, show that the following problem 1 minx, ||x – all +A ||x||2 has the optimal solution if ||a||2 A. xopt def 0, 1 ||a|l2.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
1
Transcribed Image Text:For a given vector a E R" and scalar A > 0, show that the following
problem
minx, ||x – a|l + |x||2
has the optimal solution
0,
if ||a||2 <A,
xopt def
(1- Tà) a, if ||a|l, 2 A.
|| ||2
а,
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