[3.12] Let S be a nonempty convex set in R", and let f. R" → R be defined as follows:
[3.12] Let S be a nonempty convex set in R", and let f. R" → R be defined as follows:
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
3.12
![[3.12] Let S be a nonempty convex set in R", and let f. R" -→ R be defined as
follows:
Convex Functions and Generalizations
149
f(y) = inf{ly – x|[ : xe S}.
- X
Note that f(y) gives the distance from y to the set S and is called the distance
function. Prove that fis convex.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2bc18e7a-f663-40e4-87af-7c08d362e011%2F13e1e350-3e55-4efa-9c08-5762bc75c6cb%2Fj4cu11_processed.png&w=3840&q=75)
Transcribed Image Text:[3.12] Let S be a nonempty convex set in R", and let f. R" -→ R be defined as
follows:
Convex Functions and Generalizations
149
f(y) = inf{ly – x|[ : xe S}.
- X
Note that f(y) gives the distance from y to the set S and is called the distance
function. Prove that fis convex.
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