2. Use the definition of convex functions to answer the following: (a) Show that f: RdR given by f(x₁,...,₁)= ||||= Σ is convex. (b) Show that f: RR given by f(x) = |a| is convex. Hint: You may have to break up the argument into several cases around the sign of the inputs. (c) For (b), show that f is not strongly convex. (d) Show that f: R→ R given by f(x)=√ is not convex.
2. Use the definition of convex functions to answer the following: (a) Show that f: RdR given by f(x₁,...,₁)= ||||= Σ is convex. (b) Show that f: RR given by f(x) = |a| is convex. Hint: You may have to break up the argument into several cases around the sign of the inputs. (c) For (b), show that f is not strongly convex. (d) Show that f: R→ R given by f(x)=√ is not convex.
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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Q2
Transcribed Image Text:2. Use the definition of convex functions to answer the following:
(a) Show that f: RdR given by f(x₁,...,₁)= ||||= Σ
is convex.
(b) Show that f: RR given by f(x) = |a| is convex. Hint: You may have to
break up the argument into several cases around the sign of the inputs.
(c) For (b), show that f is not strongly convex.
(d) Show that f: R→ R given by f(x)=√ is not convex.
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